Question

The adjacent sides of a parallelogram are 10m and 8m .If the distance between the longer sides is 4m,find the distance between the shorter sides.

Answer 1

ABCD be the given parallelogram, where AB = DC = 8 m, AD = BC = 10 m, and BD = 4m. Let find AC.

Let's look at the triangle ABD. Since we know the measure length of its sides, we can find the value of cos ABD by using the Law of Cosine such as:

cos ABD = (8^2 + 4^2 - 10^2)/(2 x 8 x 4) = (64 + 16 - 100)/64 = -20/64 = -0.3125

Let's say that the diagonals intersect each other at the point E. Let's look at the triangle ABE. Since we know cos ABD = -0.3125, m AB = 8 m, and m BE = 4/2 = 2 m, we can find the length measure of AE which is one half of the diagonal AC. So

(m AE)^2 = 8^2 + 2^2 - 2(8)(2)cos ABD = 64 + 4 - 32(-0.3125) = 78

m AE = √78 ≈ 8.83

Thus, m AC = 2 X 8.83 = 17.67 m