Let's Go Fly A Kite - The Solutions
March 24, 2008

When we graph the lines we see that one diagonal runs from (0, 30) to (30, 30), for a length of 30 units, and the other diagonal runs from (15, 0) to (15, 40) for a length of 40 units.

To find the area of the kite we’ll use the formula A=(1/2)d1d2

A = (1/2)(30)(40)

A = 600 sq units.

To solve this one we’ll use the Pythagorean Theorem (the distance formula can also be used).

For the shorter sides:

152 + 102  = c2

225 + 100 = 325

c = 5√13

For the longer sides:

152  + 302  = c2

225 + 900 = 1125

c = 15√5

Since there are two long sides and two short sides we know the perimeter is:

10√13 + 30√5 units

In the first problem we determined that the diagonals were 30 units and 40 units so the average of the two diagonals is (30 + 40)/2 = 35 units.

So we know that the tail Jordana made was (1.5)(35) = 52.5 units, to the nearest tenth.

To solve this one we will use the Pythagorean Theorem (with the string being the hypotenuse).

602  + x2  = 1002

3600 + x2  = 10,000

x2  = 6400

x = 80 yards

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