Question

Find the height of a triangle whose base is 2 square root 2 inches and area is 8 square root 6 square inches.

Answer 1

A=bh/2  

2A=bh

h=2A/b, we are given that A=8√6 and 2√2

h=2(8√6)/(2√2)

h=8√6/√2

h=8√(6/2)

h=8√3 in (exact)

h≈13.86 in (to nearest hundredth of an inch)

Answer 2

The height is 8 root 3 (sqrt(192)). 8 root 6 = 1/2 * 2 root 2 * x. Simplifying this gives us 8 root 6 = sqrt 2 *x. Square both sides and 64*6=2*x^2 further simplifying gives 192 = x^2, so take the squart root of both sides to get sqrt(192) which is equal to 8 root 3.