Question

The corresponding angles in △ABC are congruent to the corresponding angles in △FGH. The measures of two corresponding sides of the triangles are given:

AB=4
AC=6
FG=x+11
FH=7x

What is the length of FH?

Answer 1

since The corresponding angles in △ABC are congruent to the corresponding angles in △FGH, so they are similar triangles. in a similar triangles, their corresponding sides are in proportion.
so AB / AC = FG / FH
substitute the given values
4 / 6 = x + 11 / 7x
then solve for x
28x = 6x + 66
22x = 66
x = 3

so the value of FH = 7x = 7(3) = 31