The length of a rectangle 15 inch longer than twice it's width. if the perimeter is 78 inches. find the length of the retangle

Perimeter of a rectangle formula:

P = 2L + 2W

Length equals:

L = 2W + 15

Substitutute 2W + 15 for L

78 = 2 (2 (15 + W) + 2W

Multiply the inner parentheses

78 = 2 (30 + 2W) + 2W

Multiply the parentheses

78 = 60 + 4W + 2W

Add like terms

78 = 60 + 6W

Subtract 60 from both sides

18 = 6W

Divide both sides by 6

3 = W

Length equals:

2W + 15 = L

Substitute 3 for W

2 (3) + 15 = L

Multiply the parentheses

6 + 15 = L

Add like terms

21 = L