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ZanzabumX [31]
3 years ago
7

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 len

gth 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

Mathematics
2 answers:
irina1246 [14]3 years ago
7 0

Answer:

C.

Step-by-step explanation:

Lovely.

Alexxx [7]3 years ago
6 0

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.

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