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netineya [11]
3 years ago
8

Which value of x would make TV || QS? 3 8 10 11

Mathematics
2 answers:
Vanyuwa [196]3 years ago
6 0

Answer:

Option B. x = 10

Step-by-step explanation:

If TV ║ QS then triangles RTV and ΔRQS will be similar.

By the theorem of similarity corresponding sides should be in the same ratio.

Therefore, \frac{RT}{RV}=\frac{RQ}{RS}

\frac{(x + 4)}{(x -3)+(x + 4)}=\frac{(x+10)}{x+(x+10)}

\frac{x+4}{2x+1}=\frac{x+10}{2x+10}

By cross multiplication

(x + 4)(2x + 10) = (x + 10)(2x + 1)

2x² + 10x + 8x + 40 = 2x² + x + 20x + 10

18x + 40 = 21x + 10

21x - 18x = 40 - 10

3x = 30

x = 10

Option C. x = 10 is the answer.

Luba_88 [7]3 years ago
3 0

<u>Answer</u>

10



<u>Explanation</u>

For  TV || QS, triangle RTV should be similar to triangle RQS.

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

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

x² + 4x = x² - 3x + 10x - 30

4x = 7x - 30

4x - 7x = -30

-3x = -30

x = 10

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