SOLUTION: A kite has a 5-inch side and a 7-inch side. One of the diagonals is bisected by the other. The bisecting diagonal has length 8 inches. Find the length of the bisected diagonal.

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Question 1158585: A kite has a 5-inch side and a 7-inch side. One of the diagonals is bisected by the other.
The bisecting diagonal has length 8 inches. Find the length of the bisected diagonal.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Let the lengths of the two parts of the bisecting diagonal be x and (8-x).

Let y be the length of each half of the bisected diagonal. Then

(1) x and y are the legs of a right triangle with hypotenuse 5; and
(2) (8-x) and y are the legs of a right triangle with hypotenuse 7.

y%5E2+=+5%5E2-x%5E2
y%5E2+=+7%5E2-%288-x%29%5E2

25-x%5E2+=+49-%2864-16x%2Bx%5E2%29
25-x%5E2+=+-15%2B16x-x%5E2
25+=+16x-15
16x+=+40
x+=+2.5

The length of the bisected diagonal is 2x = 5.

ANSWER: 5