Problema Solution
A Rhombus has perimeter 180 cm and one of its diagonal is of length 72 cm. Find the length of the other diagonal.
Answer provided by our tutors
let
a = the wide of the rhombus, a>=0
d1 = 72 cm the diagonal of the rhombus, d1>=0
d2 = the other diagonal of the rhombus, d2>=0
the perimeter of a rhombus is 180 cm
4a = 180 => a = 180/4
a = 45 cm
the diagonals d1 and d2 of a rhombus bisect each other and are perpendicular.
using the Pythagorean Theorem we have
(d1/2)^2 + (d2/2)^2 = a^2
(72/2)^2 + (d2/2)^2 = 45^2
36^2 + (d2/2)^2 = 2025
by solving the equation we find and consider only the positive roots
d2 = 54 cm
to see the step by step solution click here:
the length of the other diagonal is 54 cm.