How to find side length of a square inside a triangle | Area of square inside a triangle

How to find side length of a square inside a triangle | Area of square inside a triangle
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triangle
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how to find the area of a triangle step by step
how to do area of triangle
find the area of a triangle step by step
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[@RobG1729]

A recent video on another channel used that ( a = bh/b + h ) without demonstrating that property of a square within a triangle as you've done so well here.
Thanks so much

[@AAZ3000]

Theorems are used the same way. Once proved and shown, they are applied in geometry problems without proving them again

[@dimuthdarshaka7985]

Sir I did this way triangle
ABC Area - ARS Area - BPS Area - QCR Area = a^2
Triangle BPS and QCR base is equal to (10-a) .
Thanks

[@marioalb9726]

Similarity of triangles:
(h-a)/a = h/b = 8/10
h/a - 1 = h/b
h/a = h/b +1
a = h / (h/b+1)
a = 8 / (8/10+1) = 80/18
a = 40/9 cm

[@marioalb9726]

Similarity of triangles:
(h-a)/a = h/b. = 8/10
(h-a) = 4/5 a
a + (h-a) = h
a + 4/5 a = 8
9/5 a = 8
a = 40/9 cm ( Solved √ )

[@miguelgnievesl6882]

Triangles ABC and ASR are similar due to their angles, therefore; If the ratio between the base and the height of triangle ABC is 4:5, then the same ratio applies to triangle ARS. Consequently, if the base = a then the height = 5a/4. Finally a + 5a/4 = 10. We obtain that a = 40/9.

[@marioalb9726]

then height = 4a/5 (not 5a/4)
Finally a + 4a/5 = 8 (not 10)
We obtain a = 40/9
or
then b-a = 5a/4 ( not height )
Finally a + 5a/4 = 10
We obtain a = 40/9

[@marioalb9726]

Similarity of triangles:
a / b = (h-a) / h
(h-a) = a. 8/10
Also:
(h-a) + a = 8
Replacing:
8/10 a + a = 8
a (1+4/5)=8
a= 8 / (1+4/5) = 8 / (9/5)
a= 40/9 cm

[@RAG981]

Label the side lengths, add up the areas =40. Works to give 40/9.

[@anthonyvalenti9093]

Well, I used area of triangle ars + area of trapezoid srcb.

[@sfratini]

Seems that you are assuming an acute triangle. Doesn't work for an obtuse triangle, unless I am missing something.

[@giuseppemalaguti435]

a=40/9

[@syedmdabid7191]

Eheu! Id est a= 40/9 unit. Responsimus.

[@yakupbuyankara5903]

a=40/9