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

b ≈ 9.4 units

Step-by-step explanation:

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

= =

Calculate WZ using Pythagoras identity in right triangle WZY

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

WZ = ≈ 7.81

Substituting value into the ratio

=

= ( cross- multiply )

5b = 46.86 ( divide both sides by 5 )

b ≈ 9.4 ( to the nearest tenth )

$12. that is my answer.