let

w = the width of the triangle, w>0

l = the length of the triangle, l>0

the perimeter is 40 means:

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

l + w = 20

l = 20 - w

the area is 96 means:

l*w = 96

plug l = 20 - w into the last equation:

(20 - w)*w = 96

by solving we find:

w1 = 8

w2 = 12

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

for w = 8 we have l = 20 - 8 = 12

for w = 12 we have l = 20 - 12 = 8

the dimensions of the rectangle are 8 and 12.