a paper hat is folded into the shape of a kite, as shown. what total length of ribbon is needed to line the…

Explanation:

Step1: Set up equation for equal - length sides of kite

In a kite, two pairs of adjacent sides are equal. Assuming the two long sides are equal, we set up the equation (3x + 5=5x + 1). [3x + 5=5x + 1]

Step2: Solve the equation for (x)

Subtract (3x) from both sides: (5 = 2x+1). Then subtract 1 from both sides: (4 = 2x). Divide both sides by 2, we get (x = 2). [ \begin{align*} 5-1&=2x\ 4&=2x\ x&=2 \end{align*} ]

Step3: Find the length of one long side

Substitute (x = 2) into the expression for the long - side length. Let's use (3x + 5), then (3\times2+5=6 + 5=11) inches. [3x+5=3\times2 + 5=11]

Step4: Calculate the total length of the two long sides

Since we need to line the two long sides, the total length is (2\times11 = 22) inches. [2\times11=22]

Answer:

22 in.