The area of the rectangle is 24, what is the perimeter? (HINT: think quadratic equation)
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- เผยแพร่เมื่อ 30 พ.ย. 2022
- How to solve an algebra word problem - find the perimeter of a rectangle given the area.
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Yo dude ty so much i forgot this during the year but since im studying for finals I need to learn this but you explained this really well.
I managed x squared + x. 5x =24
But forgot my school Quadratic stuff.
So failed…but I was pleased with the little conceptual jump there!
The fascinating question would be to not discard the -ve length answer….
No calculator needed:
Area = 24 units² = W . (W+5) so W² + 5W = 24 or W² + 5W - 24 = 0 factoring ( W + 8 ) . ( W - 3 ) = 0
so W = -8 or W = 3
Negative solution is not possible so W = 3 units and L = W + 5 = 3 + 5 = 8 units
Checking: 3 . 8 = 24 units² -> OK.
Perimeter = 2 . ( L + W ) = 2 . ( 3 + 8 ) = 22 units
Factoring, when possible, is the most common way to get to the answer; however, if factoring is not possible, not only will using the quadratic formula work, completing the square is another tool to get to the answer.
Factor x square + 5x - 24 = 0 Eliminate the negative one and then x must be 3 then substitute and get P=22
I solved it by looking at the area 24, thinking that is either 3 x 8, 12 x 2 or 6 x 4... 8 - 3 = 5, so that fits the bill, 8+3=11 multiply that by 2 and you have 22.
So, the actual problem is NOT 'area of the rectangle is 24, what is the perimeter?'. Many possible answers to that question!!! Sides are 6 and 4: perimeter is 20. Sides are 24 and 1: perimeter is 50! and so on. Gotta figure that the question is actually this: "Given a rectangle with one side of length x, another side of lenght x + 5, and an area of 24, what is the perimeter?"
I was thinking the same thing until I saw the drawing of the rectangle.
Found quickly it just looking factors of 24 that had a difference of 5. Quadratic formula comes up with the same result. X = 3, X + 5 = 8. The perimeter is 22 either way.
Actually I did use the quadratic formula and I got the correct result within a minute. I don’t see what’s the problem of using the quadratic formula vs factoring or anything else. The result is what really counts.
There are many problems that must be factored that don't involve the quadratic formula.
Awsome
x•(x+5)=24
X^2+5x-24=0
(x+8)(x-3)=0
X=-8 is null x=3
Width=3 length=8 perimeter=2(l+w)=22 .. At first I misread .. But checking fixed my mistake.
I came up with 22. I was not able to solve this using algebra.
OK. Now I get it. I failed to put 0 at the other side of the equal sign.
120
X=3.5
Keep in mind there are general fundamentals of the laws of physics
2 ( L+b) = 22
It's John's show of course; in the time it takes to send viewers to go learn this/that He could have just demo'ed the procedure.
@@robertakerman3570 Agreed.
It took 3 seconds, ish. Quadratic equations?
I have very long 1st's. My 2nd's take much longer(ha-ha)
I'll say 20 at a glance
Stars 5 minutes and 20 seconds into the video. Good video. Takes too much time talking about other stuff eg stars smile faces.
You make math even more boring. Stop talking so much and get to the point and teaching how to solve bro.
Now if x was 2 that would make area 14 (wrong)
If x was 3 that would make area 24 $BINGO$
Now I will watch the video
This is the guess it and try it method. Spreadsheet could not do this example faster.
what a confusing explaination. Could have been simplified by keeping it simple. Too much bragging for the first good 3 minutes. wow...