Question

You are helping some friends assemble a kite. They want to add a ribbon around the outside of the kite using the lengths indicated in the diagram. The lengths given in the diagram are in inches.

How many inches of ribbon do you need to go the entire way around the kite?

Answer in a complete sentence. Provide supporting work in your solution.

Answer 1

• 5x=3x+12
• 2x=12
• x=6

And

• 11y-22=7y-6
• 4y=16
• y=4

So

• 7y-6=7(4)-6=28-6=22
• 5x=5(6)=30

Perimeter:-

• 2(30)+2(22)
• 2(30+22)
• 2(52)
• 104in

Answer 2

104 inches

Explanation:

A kite has two pairs of consecutive, congruent sides.

Therefore, BC = AB and AD = DC

We can use this to determine the values of x and y, and then the perimeter of the kite.

If BC = AB

⇒ 5x = 3x + 12

Subtract 3x from both sides:

⇒ 2x = 12

Divide both sides by 2

⇒ x = 6

If AD = DC

⇒ 11y - 22 = 7y - 6

Subtract 7y from both sides:

⇒ 4y - 22 = -6

Add 22 to both sides:

⇒ 4y = 16

Divide both sides by 4:

⇒ y = 4

As BC = AB and AD = DC

⇒ perimeter = 2 (BC + AD)

= 2 (5x + 11y - 22)

Substituting found values of x and y:

⇒ perimeter = 2 (5(6) + 11(4) - 22)

= 2 (30 + 44 - 22)

= 2 (52)

= 104 inches