Question

We are currently learning triangle similarity and about dilations in geometry. We have been using cross multiplying to figure these out but this one has me stumped. Please help!

Answer 1

Took me a minute to think.

Form ratios.

x, the small triangle, forms a ratio with 6, the big triangle.

The part of the side that is equal(with the dash) that is part of the small triangle is equal to 6-x, the big triangle.

Yes, you can cross-multiply here!

$\frac{6}{x} = \frac{8}{6-x}$

Now, cross multiply.
P.S. Use distributive property.

36-6x = 8x

Add 6x on both sides.

36=14x

Divide by 14 on both sides.

x = $\frac{36}{14}$ = $\frac{18}{7}$