Question

5. The measures of two sides of a parallelogram are 50 and 80 inches, while one diagonal

(the shorter one) is 90 inches long. How long is the other diagonal?

Answer 1

Other diagonal is 98.5 inches long.

Explanation:

Formula to get the measure of diagonals of a parallelogram is,

`x^2+y^2=2(a^2+b^2)`

where x and y are the lengths of the diagonals and a and b is the measure of two non parallel sides.

If a = 50 inches, b = 80 inches and x = 90 inches,

then from the given formula,

90² + y² = 2(50² + 80²)

y² = 2(2500 + 6400) - 8100

y² = 17800 - 8100

y =
`√(9700)`

y = 98.49

≈ 98.5 inches

Therefore, other diagonal of the parallelogram is 98.5 inches long.