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.

Question

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 1

the bisected diagonal=about 8.66 inches

49= (8-x)^2 + y^2

25 = x^2 + y^2

subtract

24 = -16x +64

x = 40/16 = 2.5

8-x= 5.5

y^2 = 25-x^2= 25-6.25 = 18.75

y =sqr18,75

=about 4.33

2y = about 8.66 inches

Answer 2

Let bysected diagonal is 2x. Then we have: √ (25 - x²) + √(49 - x²) = 8; 25 - x² = 64 - 16√(49 - x²) + 49 - x²;

16√(49 - x²) = 88; 49 - x² = 30.25; x² = 18.75; x = 5√3/2.

So, 2x = 5√3