Question

A parallelogram has sides with lengths of `7` and `16`. If the parallelogram's area is `28`, what is the length of its longest diagonal?

Answer 1

Length of the longest diagonal AC is 25.8213

Explanation:

Given `l = 16, w = 7, Area = 28`

Area of the parallelogram = l * h = 28
`:. BE = CF = h = (Area)/l = 28 / 16 = 1.75`

AE = DF = a = sqrt(w^2-h^2) = sqrt(7^2 - 1.75^2) = 6.777#

AF = l + a = 16 + 6.7777 = 25.7777#

Longest diagonal AC `= sqrt(AF^2 + CF^2) = sqrt(25.7777^2 + 1.75^2) = 25.8213`