Question

Triangle Z W X is shown. Angle Z W X is a right angle. An altitude is drawn from point W to point Y on side Z X to form a right angle. The length of W X is b, the length of X Y is a, the length of Y Z is 5, and the length of W Y is 6.

What is the approximate value of b, rounded to the nearest tenth?

7.2 units
7.8 units
8.6 units
9.4 units

Answer 1

b ≈ 9.4 units

Explanation:

Answer 2

b ≈ 9.4 units

Explanation:

Δ WZY and Δ XWY are similar triangles, thus the ratios of corresponding sides are equal, that is

`(XW)/(WZ)` =
`(XY)/(WY)` =
`(WY)/(ZY)`

Calculate WZ using Pythagoras identity in right triangle WZY

WZ² = 5² + 6² = 25 + 36 = 61 ( take the square root of both sides )

WZ =
`√(61)` ≈ 7.81

Substituting value into the ratio

`(XW)/(WZ)` =
`(WY)/(ZY)`

`(b)/(7.81)` =
`(6)/(5)` ( cross- multiply )

5b = 46.86 ( divide both sides by 5 )

b ≈ 9.4 ( to the nearest tenth )