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 lengt

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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 lengt

h 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

1 answer:

CaHeK987 [17] · Answer 1 · 2022-12-29T16:41:30+03:00

The value of x that would make line segment T V is parallel to line segment Q S is where x = 10. (Option C)

<h3>What is a line segment?</h3>

In Mathematics, a Line Segment is a part of a line that has two endpoints.

The difference between a line segment and a line is that while the former has a starting and an endpoint, the latter does not. See the attached image.

<h3>What is the Step by Step solution to the above problem?</h3>

Step 1

Note that if QS is Parallel to TV, then both sides of the triangle must be proportionally divided by TV.

That is: RV/VS = RT/TQ.

Step 2 - replace the segments by the relevant equations

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

Step 3 - Cross Multiply

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

Removing the parentheses, we have

X² +4X = X² +7X -30; Subtract X² from both sides and we have;

4X = 7X - 30

<h3>Step 3 - Collect like terms by cross multiplying</h3>