Parallelograms

Question

The perimeter of a rhombus is 40. If the measure of the short diagonal is 12, find the measure of the longer diagonal.

Answer 1

A rhombus by definition has four equal sides. Therefore, if the perimeter is 40, then each side is 5.  10+10+10+10=40

When a diagonal is put into a rhombus, it creates two concurrent triangles.  We need to find the height of triangle JKL.  Use Pythagorean theorem and cut the length of the diagonal in half.  10²+x²=10²

X=8

Since the longer diagonal is twice that of the shorter length, we double the value of X.

8x2=16.

 

The measure of the longer diagonal is 16.