Question

question 7 of 50
the value of x is:
triangle with right angle, 45° angle, hypotenuse 8√2, leg x
options: 8√3, 8, 16, 4, 8√2

Explanation:

Step1: Identify Triangle Type

The triangle is a right - angled isosceles triangle (one angle is \(45^{\circ}\), one is \(90^{\circ}\), so the third angle is also \(45^{\circ}\)). In a \(45 - 45-90\) triangle, the legs are equal, and the hypotenuse \(h\) is related to the leg \(l\) by \(h = l\sqrt{2}\).

Step2: Solve for \(x\)

Given the hypotenuse \(h = 8\sqrt{2}\). From the formula \(h=l\sqrt{2}\), we can solve for the leg \(l\) (which is \(x\) here).
We know that \(l=\frac{h}{\sqrt{2}}\). Substitute \(h = 8\sqrt{2}\) into the formula:
\(x=\frac{8\sqrt{2}}{\sqrt{2}}\)
The \(\sqrt{2}\) in the numerator and denominator cancels out, so \(x = 8\).

Answer:

8