7.) Manuel is making a kite. He cuts out a piece of cloth in the shape shown. He uses two sticks as supports. The vertical stick is 90 cm long, and the horizontal stick is 80 cm long. They intersect at a right angle 60 cm from the bottom of the vertical stick. The vertical stick bisects the horizontal stick, as shown. Manuel wants to add a border around the perimeter of the kite. What is the length of material Manuel will need for the border? Show your work. Round your answer to the nearest centimeter.

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rahulnair123437 rahulnair123437 · Answer 1 · 2020-04-04T09:00:17+02:00

Manuel will need the length of the border material to be 244 cm.

Step-by-step explanation:

Step 1:

First, we need to determine the lengths of the sides. Assume the upper side is a and the lower side is b.

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of the triangle.

The upper triangles have sides measuring 30 cm and 40 cm. The upper side is the hypotenuse of this triangle (a).

[tex]a=\sqrt{30^{2} +40^{2}} = \sqrt{2500} = 50.[/tex]

The lower triangles have sides measuring 60 cm and 40 cm. The lower side is the hypotenuse of the lower triangle (b).

[tex]b=\sqrt{60^{2} +40^{2}} = \sqrt{5200} = 72.111.[/tex]

Step 2:

The perimeter of a kite [tex]= 2(a+b) = 2(50+72.111) = 244.222.[/tex]

Rounding the value of 244.222, we get 244 cm.

So Manuel will need the length of the material to be 244 cm.