Question

A parallelogram has two of its adjacent sides measuring 13 each. Find the sum of the squares of its diagonals

Answer 1

all sides of parellelogram will be equal and hence diagonals will be perpendicular bisector of each other
let 2 diagonals be 2x and 2y
x^2+y^2=13^2
multiplying both sides by 2 we get
2(x^2+y^2)=13^2 *2
2x^2+2y^2=169*2
=338

Answer 2

The sum of diagonals of parallelogram is 676.

A parallelogram has two of its adjacent sides measuring 13 each.

We have to find the sum of square of its diagonals.

• In case of parallelogram, “The sum of square of all sides of a parallelogram equals to the sum of square of its diagonals.”
• In short, If ABCD is ||gm then, AB² + BC² + CD² + AD² = AC² + BD²

Here, parallelogram has two of its adjacent sides measuring 13 each.

means, AB = 13 , BC = 13

but we know,

AB = CD and BC = AD [opposite sides are equal in parallelogram ]

∴ AB = BC = CD = DA = 13.

Now, 13² + 13² + 13² + 13² = (AC² + BD²)

⇒4 × 13² = 676 = (AC² + BD²)

Therefore the sum of diagonals of parallelogram is 676.

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