Question

a kite has a perimeter of 108 feet. one of the longer sides measures 30 feet. what are the lengths of the other three sides? 24 feet, 24 feet, 30 feet 24 feet, 30 feet, 30 feet 26 feet, 26 feet, 26 feet 30 feet, 48 feet, 48 feet

Explanation:

Step1: Recall the property of a kite

A kite has two pairs of adjacent sides that are equal. Let the longer side be \(a = 30\) feet. Let the shorter side be \(b\).

Step2: Use the perimeter formula

The perimeter \(P\) of a kite is \(P=2(a + b)\). Given \(P = 108\) feet and \(a = 30\) feet. Substitute into the formula: \(108=2(30 + b)\).
First, divide both sides by 2: \(\frac{108}{2}=30 + b\), so \(54=30 + b\).
Then, solve for \(b\): \(b=54 - 30=24\) feet.

So the lengths of the sides are two sides of \(30\) feet and two sides of \(24\) feet.

Answer:

24 feet, 30 feet, 30 feet (the second option)