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
30 feet, 48 feet, 48 feet

Explanation:

Step1: Recall kite - side property

A kite has two pairs of adjacent sides that are equal. Let the length of the given longer side be $a = 30$ feet. Let the length of the other adjacent - side pair be $b$.

Step2: Use perimeter formula

The perimeter $P$ of a kite is given by $P=2a + 2b$. We know that $P = 108$ feet and $a = 30$ feet. Substitute these values into the formula: $108=2\times30 + 2b$.

Step3: Solve for $b$

First, simplify the right - hand side of the equation: $108 = 60+2b$. Then subtract 60 from both sides: $108 - 60=2b$, so $48 = 2b$. Divide both sides by 2: $b = 24$ feet.

Answer:

24 feet, 24 feet, 30 feet