Question

What is the value of x? Enter your answer in the box. x =

Answer 1

Answer:

Step-by-step explanation:

The two triangles are similar and therefore we can set up a proportion

9/(9 + 72) = (3x - 20)/(3x - 20 + 56)       Combine like terms on the right

9/(81) = (3x - 20)/(3x + 36)                      Cross multiply

9(3x + 36) = 81 (3x - 20)                         Remove the brackets.

27x + 324 +1620 = 243x                        Add 1620 to both sides

27x + 324 + 1620 = 243x                       Subtract 27x from both

1944 = 216x                                            divide both sides by 216

x = 9                                  

If you feel comfortable canceling the size of the numbers can be reduced.

9/81 = 1/9

1/9 = (3x - 20)/(3x + 36)

3x + 36 = 9(3x - 20)

3x + 36 = 27x - 180

36 + 180 = 24x

216 = 24x

216/24 = x

x = 9

There is another cancelation possible, but this is simple enough.