Question

1. math on the spot alicia is using a pattern to make a kite and she must cover the outer edges with a cloth binding. there are 2 feet of binding in one package. what is the total amount of binding needed to cover the edges of the kite? how many packages of binding must alicia buy?

Explanation:

Step1: Identify congruent kite sides

A kite has 2 pairs of congruent adjacent sides: $AB=BC$, $AD=DC$.

Step2: Calculate side lengths

First, find $AB$ using Pythagoras in $\triangle AEB$:
$AB = \sqrt{AE^2 + BE^2} = \sqrt{12^2 + 7^2} = \sqrt{144+49} = \sqrt{193} \approx 13.89$ in
Find $AD$ using Pythagoras in $\triangle AED$:
$AD = \sqrt{AE^2 + ED^2} = \sqrt{12^2 + 20^2} = \sqrt{144+400} = \sqrt{544} \approx 23.32$ in

Step3: Compute total binding (perimeter)

Perimeter $P = 2(AB + AD) = 2(13.89 + 23.32) = 2(37.21) = 74.42$ in

Step4: Convert package size to inches

2 feet = $2 \times 12 = 24$ in per package

Step5: Calculate number of packages

Number of packages = $\lceil \frac{74.42}{24}
ceil = \lceil 3.10
ceil = 4$ (round up to full packages)

Answer:

Total binding needed: approximately 74.42 inches
Number of packages Alicia must buy: 4