Question

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the 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.
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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 =\square

Explanation:

Step1: Identify Similar Triangles

In right triangle \( MNP \) with altitude \( MO \), triangles \( MNP \), \( MOP \), and \( NMP \) are similar (by AA similarity, as right angles and common angles exist). So, the ratio of corresponding sides is equal. Specifically, for similar triangles \( MOP \) and \( MNP \), we have \(\frac{OP}{MP}=\frac{MP}{NP}\).

Step2: Substitute Known Values

We know \( MP = 5 \), \( NP = 7 \), and \( OP = x \). Substituting into the proportion: \(\frac{x}{5}=\frac{5}{7}\).

Step3: Solve for \( x \)

Cross - multiply: \( 7x = 5\times5=25 \). Then, \( x=\frac{25}{7}\approx3.6 \) (rounded to the nearest tenth).

Answer:

\( 3.6 \)