the perimeter of a rectangle is 38 meters. if the width is increased by two meters and the length is decreased by 3 meters the rectangle becomes a square. find the perimeter of the square

Answer 1

Hi Riley J

36 is the Perimeter of the Square

Perimeter of the rectangle is 38

Perimeter of a rectangle = 2L + 2W where L is the length and W is the widith

We are given the perimeter so

38 = 2L + 2W

Divide both sides by 2

19 = L + W

So

19 - W = L

We are also given if the Length is decreased by 3 and the width increase by 2 or

L - 3

and

W + 2

The Rectangle becomes a Square

In a Square all the sides are equal so

L - 3 = W + 2 for a square

Since we can make a substitution for L based on the information above from the rectangle we can set up our equations in terms of W and find W.

19 - W = L

Then

(19 - W) - 3 = W + 2

19 - W - 3 = W + 2

16 - W = W + 2

Isolate the variable on one side of the equation

16 = W + W + 2

16 = 2W + 2

Subtract 2 from both sides of the equation

16 - 2 = 2W

14 = 2W

Divide both sides by 2

7 = W

To get the side of the square we need to find the sides of the rectangle

L = 19 - W = 19 - 7 = 12

W = 7

The sides of the square are equal and

L - 3 = W + 2

12 - 3 = 7 + 2

9 = 9

The Perimeter of the Square is 4s = 4(9) = 36

I hope this helps