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Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of S T is 9 and the length of T Q is 16. The length of S R is x. What is the value of x? 12 units 15 units 20 units 24 units

2 Answers

0 votes

Answer:

b

Explanation:

1 vote

Answer:

Option B.

Explanation:

It is given that ΔSRQ is a right angle triangle, ∠SRQ is right angle.

RT is altitude on side SQ, ST=9, TQ=16 and SR=x.

In ΔSRQ and ΔSTR,


m\angle S=m\angle S (Reflexive property)


m\angle R=m\angle T (Right angle)

By AA property of similarity,


\triangle SRQ\sim \triangle STR

Corresponding parts of similar triangles are proportional.


(SR)/(SQ)=(ST)/(SR)

Substitute the given values.


(x)/(9+16)=(9)/(x)


(x)/(25)=(9)/(x)

On cross multiplication we get


x^2=25* 9


x^2=225

Taking square root on both sides.


x=√(225)


x=15

The value of x is 15. Therefore, the correct option is B.

User Boomerang
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