What is the scale factor?
please help!

Answers:

Work Shown:

To find the scale factor, we divide a side of triangle MNO over a corresponding side of triangle FGH. We can only pick the horizontal bottom sides since we don't know what x is yet.

scale factor = ON/HG = 15/9 = (5*3)/(3*3) = 5/3

In decimal form, this is approximately 5/3 = 1.67; however, I find it's better to stick with the fraction since it's exact.

Let's solve for x

One way to do so is to follow these steps

(FG)/(MN) = (HG)/(ON)

6/x = 9/15

6*15 = x*9 cross multiply

90 = 9x

9x = 90

x = 90/9

x = 10

Or we could solve like this

(FG)/(HG) = (MN)/(ON)

6/9 = x/15

6*15 = 9x

90 = 9x

9x = 90

x = 90/9

x = 10

We end up with the same result because we got to 90 = 9x after cross multiplying, which was found in the previous set of steps as well. There are other ways to solve using a proportion. But they should all lead to x = 10.

Note how,

MN/FG = 10/6 = (5*2)/(3*2) = 5/3

which was the scale factor we found earlier

On the left:18 in^2

Area of rectangle: 96in^2

Triangle on right: 18

Full figure area = 132inches^2