Question

In the diagram below of triangle E, F, GEFG, HH is the midpoint of start overline, E, G, end overline
EG
and II is the midpoint of start overline, F, G, end overline
FG
. If H, I, equals, minus, 4, x, plus, 45HI=−4x+45, and E, F, equals, 25, plus, 5, xEF=25+5x, what is the measure of start overline, H, I, end overline
HI
?

Answer 1

H and I are midpoints of EG and FG, so HI is the midsegment parallel to EF and equals half of EF. Thus

-4x + 45 = (1/2)(25 + 5x).

Multiply by 2: -8x + 90 = 25 + 5x → -13x = -65 → x = 5.

Then HI = -4(5) + 45 = 25.

Answer: HI = 25.