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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, the length of T Q is 16, and the length of R Q is x.
What is the value of x?

12 units
15 units
20 units
24 units

Respuesta :

scentsyaimee

Answer:

the actual answer is 20 units

Step-by-step explanation:

onyebuchinnaji

The value of x which is equal to length RQ is 20 units.

The given parameters;

  • Length of ST = 9
  • Length of TQ = 16
  • Length of RQ = x

From the given triangle we can apply similar triangle property as follows;

[tex]\frac{base \ of \ triangle \ SRQ}{hypotenuse \ of \ triangle \ SRQ} = \frac{base \ of \ triangle \ RTQ}{hypotenuse \ of \ triangle \ RTQ} \\\\\frac{RQ}{SQ} = \frac{TQ}{RQ} \\\\\frac{x}{(9 + 16)} = \frac{16}{x} \\\\x^2 = 25 \times 16\\\\x = \sqrt{25 \times 16} \\\\x = 5 \times 4\\\\x = 20 \ units[/tex]

Thus, the value of x which is equal to length RQ is 20 units.

Learn more about similar triangles here: https://brainly.com/question/11899908

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