SOLUTION: Please help me this problem it reads on the home woke sheet What are the side lengths of the rectangle? Area=40 in. Perimeter=48 in.

Algebra ->  Rectangles -> SOLUTION: Please help me this problem it reads on the home woke sheet What are the side lengths of the rectangle? Area=40 in. Perimeter=48 in.       Log On


   

Question 961523: Please help me this problem it reads on the home woke sheet
What are the side lengths of the rectangle? Area=40 in. Perimeter=48 in.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Known: A, area and p, perimeter of a rectangle.
Unknown: x and y dimensions.

system%28xy=A%2C2x%2B2y=p%29
y=A%2Fx
2x%2B2%28A%2Fx%29=p
*

2x%5E2%2Fx%2B2A=px
2x%5E2-px%2B2A=0
and you can continue with this in symbolic form, but you can find the specific result for your example faster if you substitute the given A and p NOW.

2x%5E2-48x%2B2%2A40=0
x%5E2-24x%2B40=0
START FIX: x=%2824%2B-+sqrt%2824%5E2-4%2A40%29%29%2F2
x=%2824%2B-+sqrt%28416%29%29%2F2
416=4*104=4*2*52=4*2*4*13=4^2*26
x=%2824%2B-+sqrt%284%5E2%2A26%29%29%2F2
x=%2824%2B-+4sqrt%2826%29%29%2F2
highlight_green%28x=12%2B-+2sqrt%2826%29%29

Take your pick for which dimension is x and which is y; but the two dimensions are highlight%2812-2sqrt%2826%29%29 and highlight%2812%2B2sqrt%2826%29%29.