9. Raul's teacher purchases two rectangular paintings. The dimensions of the first painting are proportional to the dimensions of the second painting. The dimensions of the first painting are 8 inches by 20 inches. One of the
dimensions of the second painting is 24 inches. Which length, in inches, could be the unknown dimension of the
second painting?

(A) 4
(B)6 2/4
(C)9 3/5
(D)12

(c) 9 3/5

Step-by-step explanation:

This is a ratio question. We can work with the dimensions as fractions and solve through cross-multiplication.

Dimensions of the first painting:

8/20 in.

Possible dimensions of the second painting:

24/x in.

x/24 in.

There are two options, because the given 24 inches may be either a length or width of the painting.

Now, we can use cross-multiplication to try to find x in both scenarios.

Scenario #1

8/20=24/x

8x=480

x=60 in.

60 in. is not an answer. Let's try the other scenario.

Scenario #2

8/20=x/24

192=20x

9.6 in.=x

9.6 can also be written as 9 3/5, which is option C.

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.