Question

If the measure of one side of a square is increased by 2 centimeters and the measure of the adjacent side is decreased by 2 centimeters, the area of the resulting rectangle is 32 square centimeters. Find the measure of one side of the square.

Answer 1

Answer:

8cm

Step-by-step explanation:

1. 32/4=8

So each side must equal 8.

Answer 2

Answer:

One of the sides is approximately 3 centimeters.

Step-by-step explanation:

We know that a square has equivalent sides, which we are gonna call $x$.

If one side increases by 2 centimeters, this can be represented as

$x+2$

If the adjacent side decreases by 2 centimeters, its representation is

$x-2$

So, the area of the new figure is

$A=(x+2)(x-2)$

Which, according to the problem, equals 32 square centimeters.

$(x+2)(x-2)=32$

Let's solve this equation, first we need to apply the distributive property

$(x+2)(x-2)=32\\x^{2} -2x+2x+4=32\\x^{2} +4=32\\x^{2} =32-4=28\\x=\sqrt{28}\\ x \approx 5$

We replace this in one of the sides expressions

$x-2=5-2=3$

Therefore, one of the sides is approximately 3 centimeters.