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 kite properties

A kite has two pairs of adjacent sides equal. Let the lengths be \( a, a, b, b \). Given perimeter \( P = 108 \) ft, and one longer side \( b = 30 \) ft.

Step2: Set up perimeter equation

Perimeter formula: \( P = 2a + 2b \). Substitute \( P = 108 \), \( b = 30 \):
\( 108 = 2a + 2(30) \)
Simplify: \( 108 = 2a + 60 \)
Subtract 60: \( 2a = 108 - 60 = 48 \)
Divide by 2: \( a = \frac{48}{2} = 24 \)
So sides are \( 24, 24, 30, 30 \).

Answer:

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