The dimensions of a rectangular garden is length is (2x+3) and the width is (3x-5). Find the length of the perimeter is equal to 26

The formula of a perimeter of a rectangle:

P = 2l + 2w

We have P = 26, l = 2x + 3 and w = 3x - 5.

Substitute:

2 (2x + 3) + 2 (3x - 5) = 26 use distributive property

(2) (2x) + (2) (3) + (2) (3x) + (2) (-5) = 26

4x + 6 + 6x - 10 = 26 combine like terms

(4x + 6x) + (6 - 10) = 26

10x - 4 = 26 add 4 to both sides

10x = 30 divide both sides by 10

x = 3

l = 2x + 3 → l = 2 (3) + 3 = 6 + 3 = 9

Answer: The length = 9