Question

A parallelogram has sides with lengths of `16` and `9`. If the parallelogram's area is `24`, what is the length of its longest diagonal?

Answer 1

Length of the longest diagonal AC = 24.9193

Explanation:

Given `l = 16, w = 9, Area = 24`

Area of the parallelogram = l * h = 24
`:. BE = CF = h = (Area)/l = 24 / 16 = 1.5`

AE = DF = a = sqrt(w^2-h^2) = sqrt(9^2 - 1.5^2) = 8.8741#

AF = l + a = 16 + 8.8741 = 24.8741#

Longest diagonal AC `= sqrt(AF^2 + CF^2) = sqrt(24.8741^2 + 1.^2) = 24.9193`