Question

select the correct answer.
what is the value of x in the triangle?
triangle with angles 45°, 45°, right angle, one leg 12√2, hypotenuse x
a. 12√2
b. 24
c. 12
d. 6√2

Explanation:

Step1: Identify Triangle Type

The triangle is a 45 - 45 - 90 triangle (right - isosceles triangle). In a 45 - 45 - 90 triangle, the legs are equal, and the hypotenuse \(c\) is related to the leg length \(a\) by the formula \(c = a\sqrt{2}\), where \(a\) is the length of each leg.

Step2: Apply the Formula

We know that one of the legs \(a = 12\sqrt{2}\). Let the hypotenuse be \(x\). From the formula \(c=a\sqrt{2}\), we substitute \(a = 12\sqrt{2}\) into the formula:

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Answer:

B. 24