Answered

For all your questions, big or small, IDNLearn.com has the answers you need. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.

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?
PLEASE HURRY

Sagot :

Sqdancefanidn

9514 1404 393

Answer:

  x = 10

Step-by-step explanation:

In order for TV to be parallel to QS, it must divide the sides of the triangle proportionally.

  RT/TQ = RV/VS

  (x+4)/(x-3) = (x+10)/(x)

  1 +7/(x-3) = 1 +10/x . . . . expand each fraction

  7/(x -3) = 10/x . . . . . . . . subtract 1

  7x = 10(x -3) . . . . . . . . . cross multiply

  30 = 3x . . . . . . . . . . . . add 30-7x, simplify

  10 = x . . . . . . . . . . . . . . divide by 3

The value of x that makes the segments parallel is 10.

_____

Alternate solution

You can cross multiply the first fraction we wrote to get ...

  x(x +4) = (x -3)(x +10)

  x^2 +4x = x^2 +7x -30 . . . eliminate parentheses

  30 = 3x . . . . . . subtract x^2+4x-30 from both sides

Answer: C. 10

Step-by-step explanation:

i got it right on the test

Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Thank you for choosing IDNLearn.com. We’re here to provide reliable answers, so please visit us again for more solutions.