Question

Find the x, Length of AD

Answer 1

x = 9

Explanation:

using Pythagoras' identity in right triangle BCD

BC² + CD² = BD²

BC² + 6² = 10²

BC² + 36 = 100 ( subtract 36 from both sides )

BC² = 64 ( take square root of both sides )

BC =
`√(64)` = 8

using Pythagoras' identity in right triangle ABC

AC² + BC² = AB²

AC² + 8² = 17²

AC² + 64 = 289 ( subtract 64 from both sides )

AC² = 225 ( take square root of both sides )

AC =
`√(225)` = 15

Then

x + 6 = 15 ( subtract 6 from both sides )

x = 9