Question

multiple-choice question
triangle with right angle, 45° angle, base 6, sides x and y
d) $x = \sqrt{6}$, $y = \sqrt{6}$
a) $x = 3\sqrt{6}$, $y = 3\sqrt{6}$
c) $x = 3\sqrt{2}$, $y = 3\sqrt{2}$
b) $x = 6\sqrt{2}$, $y = 6\sqrt{2}$
rewatch submit

Explanation:

Step1: Identify Triangle Type

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

Step2: Apply 45 - 45 - 90 Formula

Given hypotenuse \(h = 6\), let the leg be \(l\) (here \(l=x = y\)). From \(h=l\sqrt{2}\), we solve for \(l\): \(l=\frac{h}{\sqrt{2}}\). Substitute \(h = 6\): \(l=\frac{6}{\sqrt{2}}=\frac{6\sqrt{2}}{2}=3\sqrt{2}\). So \(x = y=3\sqrt{2}\).

Answer:

C) \(x = 3\sqrt{2},y = 3\sqrt{2}\)