Question

What is the value of the variables?

Answer 1

x=9 and w=12

Explanation:

To solve for w and x, create proportions between the two similar triangles.

`(Big Side)/(Big Side) =(little side)/(little side)`

where Big represents the bigger triangle an little represents the smaller triangle.

`(8)/(16)=(w)/(12+w)`

Cross multiply and solve for w.

8(12+w)=16(w)

96 + 8w = 16w

96 + 8w - 8w = 16w - 8w

96 = 8w

w=12

Repeat with a new proportion.

`(8)/(22)=(12)/(24+x)`

Cross multiply and solve for x.

8(24+x)=22(12)

192 + 8x = 264

8x = 72

x=9