let

l = the length of the rectangle, l>0

w = the width of the rectangle, w>0

P = 40 in the perimeter

A = 91 in^2 the area of the rectangle

the perimeter of a rectangle is P = 2(l + w)

2(l + w) = 40 divide both sides by 2

l + w = 20

l = 20 - w

the area of a rectangle is A = l*w

l*w = 91

plug l = 20 - w into the last equation:

(20 - w)*w = 91

by solving we find:

w1 = 13 in

w2 = 7 in

click here to see the step by step solution of the equation:

for w = 13 in the length is l = 20 - 13 = 7 in

for w = 7 in the length is l = 20 - 7 = 13 in

the dimensions of the rectangle are 13 in and 7 in.