geometry due in 30 mins please help!!

Question

The lengths of the diagonals of a parallelogram are 9.9 feet and 14 feet and they intersect at an angle of 39◦

.

Find the length of

a) the longer side of the parallelogram.

Answer in units of feet.

b) the shorter side of the parallelogram.

Answer in units of feet.

Answer 1

Intersecting diagonals form 4 triangles within the parallelogram.

The diagonals of a parallelogram bisect each other so the sides of the triangle facing each side are 4.95 and 7 feet.

The included angle between the sides of the triangles facing the shorter side of the parallelogram is 39.

The included angle between the sides of the triangles facing the longer side of the parallelogram is 180 - 39 = 141.

You can now use the law of cosines to find the lengths of the sides of the parallelogram:

shorter side^2 = sqrt(4.95^2 + 7^2 - 2*4.95*7*cos(39) )= 4.43

longer side^2 = sqrt(4.95^2 + 7^2 - 2*4.95*7*cos(141) ) = 11.29

Answer 2

If the diagonals of a parallelogram intersect in a right angle, then the parallelogram is a rhombus and the sides can be determined from the law of Pythagoras.