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 kite property

A kite has two pairs of adjacent - equal - length sides. Let the length of the shorter side be $a = 16$ cm. Let the length of the longer side be $b$.

Step2: Use perimeter formula

The perimeter $P$ of a kite is $P=2a + 2b$. We know that $P = 70$ cm and $a = 16$ cm. Substitute into the formula: $70=2\times16 + 2b$.

Step3: Simplify the equation

First, calculate $2\times16=32$. The equation becomes $70 = 32+2b$.

Step4: Solve for $b$

Subtract 32 from both sides: $70 - 32=2b$, so $38 = 2b$. Then divide both sides by 2: $b=\frac{38}{2}=19$ cm.
So the lengths of the other three sides are 16 cm, 19 cm, and 19 cm.

Answer:

16 centimeters, 19 centimeters, and 19 centimeters