Question

A parallelogram has sides with lengths of `15` and `12`. If the parallelogram's area is `72`, what is the length of its longest diagonal?

Answer 1

Longest diagonal measures 26.4376

Explanation:

Given `l = 15, w = 12, Area = 72`

Area of the parallelogram = l * h = 72
`:. BE = CF = h = (Area)/l = 72 / 15= 4.8`

AE = DF = a = sqrt(w^2-h^2) = sqrt(12^2 - 4.8^2) = 10.9982#

AF = l + a = 15 + 10.9982 = 25.9982#

Longest diagonal AC `= sqrt(AF^2 + CF^2) = sqrt(25.9982^2 + 4.8^2) = 26.4376`