Question

18,875 Learners found this answer helpful

gj is a midsegment of δhik. if hi = p + 40 and gj = p, what is the value of p? h i g j k p =

Explanation:

Step1: Recall midsegment theorem

The midsegment of a triangle is parallel to the third side and half its length. So, \( GJ=\frac{1}{2}HI \).

Step2: Substitute given values

We know \( HI = p + 40 \) and \( GJ = p \). Substitute into the formula: \( p=\frac{1}{2}(p + 40) \).

Step3: Solve for \( p \)

Multiply both sides by 2: \( 2p=p + 40 \). Subtract \( p \) from both sides: \( 2p - p=p + 40 - p \), so \( p = 40 \).

Answer:

\( 40 \)