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What is the value of x?
15 units
12 units
20 units
24 units
(Image: 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.)
To find the value of ( x ) (the length of ( S R )), we can use the Pythagorean theorem, which applies because triangle ( S R Q ) is a right triangle.
1. We know that in triangle ( S T Q ):
– ( S T = 9 ) units
– ( T Q = 16 ) units
2. First, we can calculate ( S Q ) (the length of side ( S Q )):
[
S Q = S T + T Q = 9 + 16 = 25 text{ units}
]
3. According to the Pythagorean theorem:
[
S R^2 + S T^2 = S Q^2
]
Substituting the known values:
[
x^2 + 9^2 = 25^2
]
[
x^2 + 81 = 625
]
4. Now, we solve for ( x^2 ):
[
x^2 = 625 – 81 = 544
]
5. Taking the square root gives:
[
x = sqrt{544} approx 23.32
]
Since ( x ) needs to be a value from the options given (15, 12, 20, 24), we can