Question

multiple-choice question
a right triangle with one angle 45 degrees, hypotenuse 6√2, legs x (horizontal) and y (vertical). options:
d) x=6, y=6
b) x=3√2, y=3√2
c) x=4√3, y=4√3
a) x=6√2, y=6√2
rewatch

Explanation:

Step1: Identify Triangle Type

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

Step2: Use Hypotenuse Formula

Given hypotenuse \(h = 6\sqrt{2}\), and \(h=l\sqrt{2}\) (where \(l=x = y\)). Let \(l=x=y\), then \(6\sqrt{2}=l\sqrt{2}\). Divide both sides by \(\sqrt{2}\), we get \(l = 6\). So \(x = 6\) and \(y = 6\).

Answer:

D) \(x = 6,y = 6\)