Problema Solution
if the length of the diagonal of a rectangle is 50 in. and the area is 1200 in. what are the dimensions?
Answer provided by our tutors
let
l = the length of the rectangle, l>0
w = the width of the rectangle, w>0 and l>w
d = 50 in the diagonal of the rectangle
A = 1200 in^2 the are of the rectangle
using the Pythagorean Theorem we can write
l^2 + w^2 = 50^2
the area A = l*w
l*w = 1200
l = 1200/w
plug l = 1200/w into l^2 + w^2 = 50^2
(1200/w)^2 + w^2 = 50^2
by solving we find
w1 = 40 in
w2 = 30 in
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for w = 40 in
l = 1200/40 = 30 < 40 is not the solution
for w = 30 in
l = 1200/30 = 40 in is the solution
the dimensions of the rectangle are: the width is 30 inches and the length is 40 inches.