Question

]Triangle R Q S is cut by line segment T V. Line segment T V goes from side Q R to side R S. The length of R V is x + 10, the length of V S is x, the length of R T is x + 4, and the length of T Q is x minus 3.
Which value of x would make Line segment T V is parallel to Line segment Q S?

3
8
10
11

Answer 1

The value of 'x' that would make Line segment T V is parallel to Line segment Q S is 10. Option C

How to determine the value

It is important to note that for line TV to be parallel to line QS, the sides of the triangle must be divided equally.

Thus, we have

RT/TQ = RV/VS

RT = x + 10

TQ = x - 3

RV = x + 10

VS = x

Substitute the value

$\frac{x + 4}{x-3} = \frac{x + 10}{x}$
Cross multiply

(x+ 4) × x = (x + 10) × (x-3)

x² + 4x =  x² -3x + 10x -30

Divide through by x²

4x = -3x + 10x - 30

Collect like terms

4x + 3x - 10x = - 30

-3x = -30

x = -30/ -3

x = 10

Thus, the value of 'x' that would make Line segment T V is parallel to Line segment Q S is 10 Option C

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