Can you find the area of the Blue Square? | (Rectangle) |

Learn how to find the area of the Blue Square. Important Geometry and Algebra skills are also explained: Pythagorean theorem; area of the square formula; area of the rectangle formula. Step-by-step tutorial by PreMath.com
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Can you find the area of the Blue Square? | (Rectangle) | #math #maths | #geometry
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[@GablesDude]

This was great! Thank you for your clear instructions!

[@PreMath]

Glad to hear that!
You are very welcome!
Thanks for the feedback ❤️

[@yalchingedikgedik8007]

Thanks Sir
Thanks PreMath
That’s very good and enjoyable
Good luck with glades
❤❤❤❤❤❤❤

[@marioalb9726]

A₁ = 15 cm² = b.h = 5h
h = 3 cm
Pytagorean theorem:
(s-3)²+(s-5)²=10²
(s²-6s+9)+(s²-10s+25)=100
2s² - 16s + 34 = 100
s² - 8s - 33 = 0
s = 11 cm
s² = 121 cm² ( Solved √ )

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@alastairjames8723]

X=-3 represents a square whose top right corner is the bottom left corner of the green rectangle and whose bottom left corner is the point B. Don't reject it just because it's 'out of the box'

[@quigonkenny]

Green rectangle:
Aɢ = hw
15 = h(5)
h = 15/5 = 3
Draw CA, where C is the point on the top side of the blue square where BC and CA are perpendicular. If s is the side length of the blue square, then by observation, BC = s-5 and CA = s-3.
Triangle ∆ABC:
BC² + CA² = AB²
(s-5)² + (s-3)² = 10³
s² - 10s + 25 + s² - 6s + 9 = 100
2s² -16s - 66 = 0
s² - 8s - 33 = 0
(s-11)(s+3) = 0
s = 11 | s = -3 ❌ s > 0
Blue square:
Aʙ = s² = 11² = 121 cm²

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@sorourhashemi3249]

Easy

[@PreMath]

Thanks for the feedback ❤️

[@devondevon4366]

121
The width of the rectangle = 3 (15/5)
Draw a line from the edge of the rectangle to the square to
form a right triangle .
Let the length of the square = n,
then the bases of the triangle are , n-5, and n-3.
Hence, 10^2 = (n-5)^2 + (n-3)^2
=n^2 + 25-10n + n^2 +9-6n
=2n^2 + 34- 16n
50 = n^2 + 17-8n
0 = n^2 - 33-8n
0 = (n-11) (n+3)
11=n
121= n^2

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@sergioaiex3966]

Solution:
A = Lenght × Width
15 = 5 × W
W = 3 cm
Applying Pythagorean Theorem, we'll have:
(a - 5)² + (a - 3)² = 10²
a² - 10a + 25 + a² - 6a + 9 = 100
2a² - 16a + 34 = 100
2a² - 16a - 66 = 0 (÷2)
a² - 8a - 33 = 0
a = [8 ± √(64 + 132)]/2
a = [8 ± 14]/2
a = 11
A = a²
A = (11)²
A = 121 cm²
=========

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@pas6295]

First ly name the points of intersection as A. B. C. D. E And F. Extend EF to meet BC at G. Now the four sides of the square are AB. BC. CD. and. DA. Let that be =X cms. Take the green figure Area is 25 cm^2. One side is 3 cm. Hence the other side Namely ED and FH =3cm. Now the triangle BFG you have BG as =X-3and FG as =X-5. So in the triangle Rt angle FB^2= (x-3)^2+(x-5)^2.
100=2x^2-16x+44.
So 2x^2-16x=56. By dividing by 2 .We have. X^2-8X-28=0. So in that Quadratic equation you get two values. Take the positive one as length is positive. That when multiples by X itself becomes the area.

[@Waldlaeufer70]

(a - 5)² + (a - 3)² = 10²
a² - 10a + 25 + a² - 6a + 9 = 100
2a² - 16a + 34 = 100
a² - 8a + 17 = 50
a² - 8a = 33
a² - 8a + 16 = 33 + 16 = 49
(a - 4)² = 49
a - 4 = 7 (negative solution invalid)
a = 11
A(square) = 11² = 121 [cm²]

[@satrajitghosh8162]

green rectangle is of 5 cm long and 3 cm high
Side of blue square be a
This implies
( a - 5)^2 + ( a - 3)^2 = 10 ^2
2 a ^2 - 16 a + 34 = 100
a^2 - 8 a + 64 = 130
a = 8 + √ (130)
Hereby a^2 = 194 + 16 √ (130)

[@batavuskoga]

I made one stupid mistake
(x-3)²+(x-5)²=10²
x²-6x+9=x²-10x+25=100
By adding I made the mistake
2x²-16x+36=100 instead of 2x²-16x+34=100
Buthey, this happens to all of us. We're all human beings.
One of the best math channels on youtube, clear explanation. You can't say that of some other math channels

[@PreMath]

Excellent!
Glad to hear that!
Thanks for the feedback ❤️🙏

[@Birol731]

My way of solution ▶
Agreen= 15 cm²
x= 5 cm
⇒
15= 5y
y= 3 cm
[AB]= 10 cm
The length [AB] is the hypothenuse of a right triangle:
the length of the blue square a
the base of this rectangular = a-5
the height of this triangular= a-3
By applyling the Pythagorean theorem we get:
10²= (a-3)²+(a-5)²
100= a²-6a+9+a²-10a+25
2a²-16a-66=0
a²-8a-33=0
Δ= 196
√Δ= 14
⇒
a₁= (8+14)/2
a₁= 11 cm
a₂= (8-14)/2
a₂= -3 < 0 ❌
⇒
a= 11 cm
Asquare= 11²
Asquare= 121 cm²

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@gelbkehlchen]

Solution:
a = horizontal side of the green rectangle = 5,
b = vertical side of the green rectangle = 15/5 = 3,
x = side of the blue square.
Pythagoras:
(x-5)²+(x-3)² = 10² ⟹
x²-10x+25+x²-6x+9 = 100 |-100 ⟹
2x²-16x-66 = 0 |/2 ⟹
x²-8x-33 = 0 |p-q-formula ⟹
x1/2 = 4±√(16+33) = 4±7 ⟹
x1 = 4+7 = 11 and x2 = 4-7 = -3 [not allowed in geometry] ⟹
Blue square area = 11² = 121[cm²]

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@jamestalbott4499]

Thank you!

[@PreMath]

You are very welcome!
Thanks for the feedback ❤️

[@calvinmasters6159]

Thank you.
More please.

[@PreMath]

More to come!
You are very welcome!
Thanks for the feedback ❤️

[@cyruschang1904]

(x - 3)^2 + (x - 5)^2 = 10^2
2x^2 - 16x - 66 = 0
x^2 - 8x - 33 = 0
x = (4 + ✓49) cm = 11 cm
area = (11 cm)^2 = 121 cm^2

[@countysecession]

Knew the answer by looking. A right triangle with a hypotenuse of 10 gives it away.

[@PreMath]

Excellent!
Thanks for the feedback ❤️

[@phungpham1725]

I agree with you! It is indeed a 6-8-10 triangle in this problem😊!

[@prossvay8744]

Let x is the side of square
So (x-3)^2+(x-5)^2=10^2
So x=11cm
Area of the blue square=11^2=121 cm^2.❤❤❤

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@AmirgabYT2185]

S=121 cm²

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@santiagoarosam430]

(a-5)²+[a-(15/5)]²=10²→ a=11→ a²=121 = Área del cuadrado azul.
Gracias y saludos.

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@himo3485]

15/5=3 5+x=3+y y=x+2
x²+(x+2)²=10² 2x²+4x+4=100 2x²+4x-96=0 x²+2x-48=0
(x+8)(x-6)=0 x>0 , x=6 y=8 5+6=3+8=11
Blue Square area = 11*11 = 121cm²

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@joeschmo622]

✨Magic!✨
I used s instead of x, but yeah, got 121.

[@PreMath]

Excellent!
Thanks for the feedback ❤️

[@unknownidentity2846]

Let's find the area:
.
..
...
....
.....
The height of the green rectangle can be calculated as follows:
A = (base b)*(height h) ⇒ h = A/b = (15cm²)/(5cm) = 3cm
Now let's add point C on the right side of the blue square such that ABC is a right triangle. In this case we can apply the Pythagorean theorem and with s being the side length of the square we obtain:
AB² = AC² + BC²
AB² = (s − b)² + (s − h)²
(10cm)² = (s − 5cm)² + (s − 3cm)²
100cm² = s² − (10cm)*s + 25cm² + s² − (6cm)*s + 9cm²
0 = 2*s² − (16cm)*s − 66cm²
0 = s² − (8cm)*s − 33cm²
s = 4cm ± √[(4cm)² + 33cm²] = 4cm ± √(16cm² + 33cm²) = 4cm ± √(49cm²) = 4cm ± 7cm
Since the side length is a positive quantity, the only useful solution is:
s = 4cm + 7cm = 11cm
Now we are able to calculate the area of the blue square:
A = s² = (11cm)² = 121cm²
Best regards from Germany

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@akilamohan5919]

Simple question

[@PreMath]

Thanks for the feedback ❤️

[@marcgriselhubert3915]

Fine, that's simple.

[@PreMath]

Thanks for the feedback ❤️

[@giuseppemalaguti435]

(l-3)^2+(l-5)^2=100...l=11

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@hakopajemyan334]

121

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@LuisdeBritoCamacho]

STEP-BY-STEP RESOLUTION PROPOSAL :
01) Lets close the Rigth Triangle creating Point C.
02) BC = X
03) AC = Y
04) AB = 10
05) 100 = X^2 + Y^2
06) Square Side = 5 + Y
07) Square Side = 3 + X
08) 5 + Y = 3 + X ; Y = X - 2
09) 100 = X^2 + (X - 2)^2 ; 100 = X^2 + X^2 - 4X + 4 ; 2X^2 - 4X + 4 = 100 ; 2X^2 - 4X - 96 = 0 ; X^2 - 2X - 48 = 0
10) Two Solutions : X = - 6 or X = 8
11) So, X = 8 and Y = 6
12) Square Side = 5 + 6 = 3 + 8 = 11
13) Area = 11^2 = 121
Therefore,
OUR ANSWER :
Blue Square Area equal 121 Square Centimeters.

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@yakovspivak962]

(X-5)^2 + (X-3)^2 = 100
X = 11
S = 121

[@adgf1x]

Ar. square=11^2=121 sq.unit.

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@sergeyvinns931]

121.

[@michaeldoerr5810]

The area is 121 cm squared

[@michaeldoerr5810]

Another geometry problems that is *easier* than it looks!!!

[@PreMath]

Excellent!
Thanks for the feedback ❤️

[@wackojacko3962]

@ 7:52 is a classic example of throwing the baby out with the bathwater by the overzealous physicists in search of dark matter . ...just sayin! 🙂

[@PreMath]

😀
Thanks for the feedback ❤️

[@pas6295]

Not 25 but 15. So the other side is 3. Cms

[@misterenter-iz7rz]

(s-3)^2+(s-5)^2=100, s^2-8s-33=0, s=11 or -3, rejected, thus the answer is 121.😊

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@RAG981]

?

[@JSSTyger]

121

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@sergeyvinns931]

121.

[@PreMath]

Excellent!
Thanks for sharing ❤️

[@sergeyvinns931]

121

[@PreMath]

Excellent!
Thanks for sharing ❤️