Question

a paper hat is folded into the shape of a kite, as shown. what total length of ribbon is needed to line the two long sides of the hat? (3x + 5) in. (5x + 1) in. (2x + 1) in. 5 in. 10 in. 11 in. 20 in. 22 in.

Explanation:

Step1: Identify congruent sides in kite

A kite has two pairs of adjacent congruent sides. Assume (2x+1) and 5 are congruent: \(2x + 1 = 5\).

Step2: Solve for x

\(2x = 5 - 1 = 4\), so \(x = 2\).

Step3: Calculate lengths of other sides

For \(3x + 5\): \(3(2) + 5 = 11\) in. For \(5x + 1\): \(5(2) + 1 = 11\) in. These are the long sides.

Step4: Total length of two long sides

\(11 + 11 = 22\) in.

Answer:

22 in.