Question

Use the image to answer the question.

On right triangle upper N upper P upper M, the altitude of vertex upper M is drawn as a solid line that extends from upper M to the hypotenuse, upper N upper P. The intersection of the altitude and upper N upper P is labeled upper O.

Image Long DescriptionThe following sides of triangle upper N upper P upper M are labeled: upper M upper P is 5, and upper N upper P is 7. Upper O upper P is labeled lower x. Right angle symbols are drawn at angle upper N upper M upper P and angle upper M upper O upper P.

Given is the right triangle MNP
with altitude MO
. Find the value of x. Express your answer as a decimal rounded to the nearest tenth.

(1 point)
x=

Answer 1

Use the geometric mean property: for right triangle with altitude to the hypotenuse, (leg)^2 = (adjacent hypotenuse segment) × (hypotenuse). Thus

x = OP = MP^2 / NP = 5^2 / 7 = 25/7 ≈ 3.5714286.

Rounded to the nearest tenth: x = 3.6.