A parallelogram ABCD has the area of 40 cm2, |AB| = 8.5 cm and |BC| = 5.65 cm. Find the length of its diagonals

Answer 1

If the altitude from D to AB has length h, and meets AB at a distance x from A, then
8.5h = 40
h = 40/8.5 = 4.7
x^2 + h^2 = 5.65^2
x = 3.13
tanA = h/x = 1.5
A = 56.4°
Now use the law of cosines to find the diagonals.