Question

Which value of x would make TV || QS?

3
8
10
11

Answer 1

Option B. x = 10

Explanation:

If TV ║ QS then triangles RTV and ΔRQS will be similar.

By the theorem of similarity corresponding sides should be in the same ratio.

Therefore,
`(RT)/(RV)=(RQ)/(RS)`

`((x + 4))/((x -3)+(x + 4))=((x+10))/(x+(x+10))`

`(x+4)/(2x+1)=(x+10)/(2x+10)`

By cross multiplication

(x + 4)(2x + 10) = (x + 10)(2x + 1)

2x² + 10x + 8x + 40 = 2x² + x + 20x + 10

18x + 40 = 21x + 10

21x - 18x = 40 - 10

3x = 30

x = 10

Option C. x = 10 is the answer.

Answer 2

10

Explanation

For TV || QS, triangle RTV should be similar to triangle RQS.

(x+4)/(x-3) = (x + 10)/x

x(x + 4) = (x + 10)(x -3)

x² + 4x = x² - 3x + 10x - 30

4x = 7x - 30

4x - 7x = -30

-3x = -30

x = 10