The lengths of two adjacent sides of a parallelogram are 8 and 15. Find the sum of squares of lengths its diagonals.

Question

The lengths of two adjacent sides of a parallelogram are 8 and 15, respectively. Find the sum of squares of the lengths of the two diagonals.

Answer 1

Diagnals can be found out using cosine law but the angles will be unknown as shown below.

D1^2 = 8^2 + 15^2 - 2(8*15*Cos A) [A is the smaller angle here and D1 the smaller diagnal ]

D2^2 = 8^2 + 15^2 - 2 (8*15* Cos (180-A)) [all the angles in a parallelogram add upto 360 degree.]

Since D1^2 + D2^2 is the needed answer adding the above to gets us an answer = 578 units. [ because the terms with angles cancel each other as Cos (180-A) = -Cos (A).]