Question

A parallelogram has sides with lengths of `14` and `6`. If the parallelogram's area is `63`, what is the length of its longest diagonal?

Answer 1

Longest diagonal measures 18.5235

Explanation:

Given `l = 14, w = 6, Area = 63`

Area of the parallelogram = l * h = 63
`:. BE = CF = h = (Area)/l = 63 / 14= 4.5`

AE = DF = a = sqrt(w^2-h^2) = sqrt(6^2 - 4.5^2) = 3.9686#

AF = l + a = 14 + 3.9686 = 17.9686#

Longest diagonal AC `= sqrt(AF^2 + CF^2) = sqrt(17.9686^2 + 4.5^2) = 18.5235`