Question

In ∆FGH , FH⎯⎯⎯⎯⎯⎯∥BC⎯⎯⎯⎯⎯ , GB=14.4 , BF=4.8 , and GH=21 . What is a good estimate for the measure of CH⎯⎯⎯⎯⎯⎯ ? Multiple choice question. A) 2 B) 5 C) 10 D) 20 Find GC and CH. GC= CH=

It is on an 8.5 homework on mcgrawhill

Answer 1

By setting up a proportion based on the similarity of triangles FGH and GBC, we can solve for GC and CH. The calculations show that GC equals 6 and CH equals 15.

Step-by-step explanation:

The problem given is a geometry problem involving similar triangles. Since the line FH is parallel to BC, triangle FGH is similar to triangle GBC by the AA (Angle-Angle) similarity postulate. Using this information, we can set up a proportion using the corresponding sides of the similar triangles.

Let's denote GC as x. Then, CH would be 21 - x since GH is given as 21 and GH = GC + CH. We know that GB is 14.4 and BF is 4.8. So, the proportion will be GB/BF = GH/CH, giving us the equation 14.4/4.8 = 21/(21 - x). Solving for x gives us x = 6, hence GC = 6 and CH would then be 21 - 6 = 15.