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

Answer:

Option C.

Step-by-step explanation:

Given information: TV║QS, RV=x+10, VS=x, RT=x+4 and TQ=x-3.

Triangle Proportionality Theorem: This theorem states that if a line segment is parallel to the base of a triangle and it intersects the other two sides, then it divides those sides proportionally.

Using the Triangle Proportionality Theorem, we get

$\dfrac{RT}{TQ}=\dfrac{RV}{VS}$

Substitute the given values in the above equation.

$\dfrac{x+4}{x-3}=\dfrac{x+10}{x}$

On cross multiplication we get

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

$x^2+4x=x^2-3x+10x-30$

$x^2+4x=x^2+7x-30$

Subtract x² from both sides.

$x^2+4x-x^2=x^2+7x-30-x^2$

$4x=7x-30$

Subtract 7x from both sides.

$4x-7x=7x-30-7x$

$-3x=-30$

Divide both sides by -3.

$x=\frac{-30}{-3}$

$x=10$

The value of x is 10. Therefore, the correct option is C.

Answer 2

Answer:

C.

Step-by-step explanation:

Lovely.