Question

point h is between w and p. wh = 3n - 1 ph = 2n + 1 wp = 4n + 5 what is m\overline{wp}?

Explanation:

Step1: Use the segment - addition postulate

Since point H is between W and P, we have \(WH + PH=WP\). Substitute the given expressions: \((3n - 1)+(2n + 1)=4n + 5\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(3n-1 + 2n+1=5n\). So, \(5n=4n + 5\).

Step3: Solve for n

Subtract \(4n\) from both sides of the equation: \(5n-4n=4n + 5-4n\), which gives \(n = 5\).

Step4: Find the length of WP

Substitute \(n = 5\) into the expression for \(WP\). \(WP=4n + 5\), so \(WP=4\times5+5\).
\(WP=20 + 5=25\).

Answer:

25