A rhombus has a perimeter of 80 inches. Its longer diagonal is 32 inches. Explain why the shorter diagonal must be 24 inches.

Answer: The answer is provided below.

Step-by-step explanation:

A rhombus has 4 equal sides, therefore, since the perimeter is 80 inches, that means each side is 20 inches.

The diagonals of a rhombus bisect one another perpendicularly, so that means there are 4 congruent right triangles that are formed.

Looking at one right triangle, we can see that the side of the rhombus will be the hypotenuse which is 20 inches. One leg is also half the longer diagonal of 16 inches.

Using Pythagorean Theorem, this will be:

x² + 16² = 20²

x² + 256 = 400

x² = 144

x = 12

Since the figure gotten is half of the shorter diagonal, then the full length of the shorter diagonal will be (12*2) = 24 inches.