Question

select the correct answer.
what is the value of x?
a. 15
b. 21.2
c. 7.5
d. 10.6

Explanation:

Step1: Identify the triangle type

This is a right - angled triangle with one angle \(45^{\circ}\), so it is a \(45 - 45-90\) triangle. In a \(45 - 45-90\) triangle, the sides are in the ratio \(1:1:\sqrt{2}\). Let the hypotenuse be \(c\) and the legs be \(a\) and \(b\). Here, if we assume the legs are of length \(x\) (since the non - hypotenuse angles are \(45^{\circ}\) each, the legs are equal) and the hypotenuse \(c = 15\). Using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), and since \(a = b=x\), we have \(x^{2}+x^{2}=15^{2}\).

Step2: Solve the equation

$$
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$$

Answer:

D. 10.6