Problema Solution
A rectangle has a perimeter of 40 inches and an area of 91 square inches. What are its length and width?
Answer provided by our tutors
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.