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

In a kite, two pairs of adjacent sides 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 \(P=2a + 2b\). Given \(P = 70\) cm and \(a = 16\) cm.
Substitute into the formula: \(70=2\times16+2b\).
Simplify: \(70 = 32+2b\).
Subtract 32 from both sides: \(2b=70 - 32\).
\(2b = 38\).
Divide both sides by 2: \(b=\frac{38}{2}=19\) cm.

Answer:

16 centimeters, 19 centimeters, and 19 centimeters.