A kite has an 8-inch side and a 15-inch side, which form a right angle. Find the length of the diagonals of the kite.

Question

A kite has an 8-inch side and a 15-inch side, which form a right angle. Find the length

of the diagonals of the kite.

Answer 1

a kite has sides 15 and 8 inches

the 15 and 8 sides are at right angles

the diagonals are sqr(15^2 + 8^2) = sqr(225 +64) = sqr(289) = 17 inches

and 14 2/17 inches

the shorter diagonal = one side of a right triangle with hypotenuse = 8

one side = x, other side = y = half the shorter diagonal

8^2 = x^2 + y^2

15^2 = (17-x)^2 + y^2

-64+225 = 289 -34x

34x =128

x = 128/34 = 64/17

x = about 3.7647

x = about 3.8 inches

y = sqr(64-3.8^2)

y = 120/17

2y = 240/17 inches for the shorter diagonal

2y = 14 2/17 inches