Question

The adjacent sides of a parallelogram are 45 cm and 28 cm. Find the sum of the squares of its
diagonals.

Answer 1

let the obtuse angle be A and its opposite diagonal be x. By the cosine law:
x^2 = 45^2+28^2-2(48)(28)cosA

similarly...
y^2 = 45^2+28^2-2(48)(28)cosB

but A+B = 180
B=180-A
and cosØ = -cos(180-Ø) by the CAST rule
e.g. cos 60 = - cos120
then cos B = -cosA

x^2+y^2 = 45^2+28^2-2(48)(28)cosA + 45^2+28^2-2(48)(28)cosB
= 45^2+28^2-2(48)(28)cosA + 45^2+28^2-2(48)(28)(-cosA)

= 2(45^2+28^2)

illustrating one of the properties of parallograms