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
