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Ilia_Sergeevich [38]
3 years ago
11

The area of a square is 32 more than its perimeter. find the length of a side.

Mathematics
1 answer:
Eva8 [605]3 years ago
6 0

Answer:

<em>The length of a side of the square is 8 unit.</em>

Step-by-step explanation:

Suppose, the length of a side of the square is a unit.

<u>Formula for perimeter of square</u>:  P=4(side) = 4a

<u>Formula for area of square</u>:   A=(side)^2 = a^2

Given that, the area is 32 more than the perimeter. So, the equation will be......

a^2= 4a+32

Moving all terms to the left side, we will get.....

a^2-4a-32=0

Now, factoring out the left side.......

a^2-8a+4a-32=0\\ \\ a(a-8)+4(a-8)=0\\ \\ (a-8)(a+4)=0

<u>Using 'zero-product property'</u>, we will get......

a-8=0\\ a=8\\ \\ and\\ \\ a+4=0\\ a=-4

<em>(Negative value is ignored as the side length can't be in negative)</em>

So, the length of a side of the square is 8 unit.

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