Question

A parallelogram has sides with lengths of `14` and `15`. If the parallelogram's area is `35`, what is the length of its longest diagonal?

Answer 1

Longest diagonal measures 28.8986

Explanation:

Given `l = 15, w = 14, Area = 35`

Area of the parallelogram = l * h = 35
`:. BE = CF = h = (Area)/l = 35 /15= 2.3333`

AE = DF = a = sqrt(w^2-h^2) = sqrt(14^2 - 2.3333^2) = 13.8042#

AF = l + a = 15 + 13.8042 = 28.8042#

Longest diagonal AC `= sqrt(AF^2 + CF^2) = sqrt(28.8042^2 + 2.3333^2) = 28.8986`