Question

the adjacent sides of a parallelogram are 45cm and 28 cm. find the sum of the squares of its diaginals.​

Answer 1

Step-by-step explanation:

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