Problema Solution
The length and width of a rectangle are in the ratio of 5:12. If the rectangle has an area of 240 square centimeters, what is the length, in centimeters, of its diagonal?
Answer provided by our tutors
let
l = the length of the rectangle, w>0
w = the width of the rectangle, l>0
the length and width of a rectangle are in the ratio of 5:12
w : l = 5 : 12 cross multiply
12w = 5l divide both sides by 12
w = (5/12)l
the rectangle has an area of 240 square centimeters
l*w = 240
plug w = (5/12)l into the last equation
l*(5/12)l = 240
by solving we find
l = 24 cm
click here to see the step by step solution of the equation
w = (5/12)*24
w = 10 cm
using the Pythagorean Theorem for the length of the diagonal d we have
d^2 = 24^2 + 10^2
d^2 = 676
d = 26 cm
the length of the diagonal is 26 centimeters.