Question

select the correct answer.
what is the value of x in the triangle?
a. 3√2
b. 3
c. 6
d. 6√2
e. 2√2

Explanation:

Step1: Identify the triangle type

The triangle is a right - angled isosceles triangle (since the non - right angles are equal). In a right - angled isosceles triangle, the legs are equal. Let the legs be \(a = x\) and \(b=x\), and the hypotenuse \(c = 3\sqrt{2}\).

Step2: Apply Pythagorean theorem

By the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Substituting \(a = x\), \(b = x\), and \(c = 3\sqrt{2}\), we get \(x^{2}+x^{2}=(3\sqrt{2})^{2}\).
Simplify the left - hand side: \(2x^{2}=9\times2\).
Divide both sides by 2: \(x^{2}=9\).
Take the square root of both sides: \(x = 3\) (we take the positive value since \(x\) represents a length).

Answer:

B. 3