Question

Geometry word problem help! triangle ABC is similar to triangle FGH with medians AP and FQ to sides BC and GH respectively, AB=9, and FG=6. If AP is 4 greater than FQ, find both medians.

Answer 1

draw it out

Answer 2

Hint : medians also scale by same factor when triangles are similar

Answer 3

\[\large \dfrac{9}{6} = \dfrac{AP}{FQ}\]

Answer 4

Hmmm. I see. Thanks!

Answer 5

But AP is 4 greater than FQ?

Answer 6

Yes so \(AP = FQ+4\)

Answer 7

\[\large \dfrac{9}{6} = \dfrac{FQ+4}{FQ}\]

cross multiply and solve \(FQ\) first

Answer 8

FQ=8?

Answer 9

Yep

Answer 10

so AP =32?

Answer 11

how ?

AP = FQ + 4
= 8 + 4
= 12

right

Answer 12

so AP = 12

Answer 13

I see. I multiplied instead.