Question

a kite has a perimeter of 70 centimeters. one of the shorter sides measures 16 centimeters. what are the lengths of the other three sides? 16 centimeters, 16 centimeters, and 19 centimeters 16 centimeters, 19 centimeters, and 19 centimeters 16 centimeters, 38 centimeters, and 38 centimeters 18 centimeters, 18 centimeters, and 18 centimeters

Explanation:

Step1: Recall the property of a kite

A kite has two pairs of adjacent sides that are equal. Let the shorter side be \(a = 16\) cm. Let the longer side be \(b\).

Step2: Use the perimeter formula

The perimeter \(P\) of a kite is \(P=2(a + b)\). Given \(P = 70\) cm and \(a = 16\) cm. Substitute into the formula: \(70=2(16 + b)\).
First, divide both sides by 2: \(\frac{70}{2}=16 + b\), so \(35=16 + b\).
Then, solve for \(b\): \(b=35 - 16=19\) cm.

Since the kite has two shorter sides (equal) and two longer sides (equal), the lengths of the sides are \(16\) cm, \(19\) cm, \(19\) cm.

Answer:

16 centimeters, 19 centimeters, and 19 centimeters