Length can be expressed as 2L + 2w = 26 since we know the total perimeter is 26 inches. Width can expressed as w = 3L - 15, since we know that it is 15 inches less than 3x the length. Then substitute the width into the length formula.
2L + 2w = 26
2L + 2(3L - 15) = 26
2L + 6L - 30 = 26
8L = 56
L = 56/8
L = 7 inches
Substitute 7 into the width formula to find width:
w = 3L - 15
w = 3 x 7 - 15
w = 6 inches
Finally use the area formula:
A = L x W
A = 7 x 6
A = 42 [tex]inches^{2}[/tex]
