Question

current attempt in progress
assuming a triangle is 45° - 45° - 90° and the hypotenuse has measure 2y, find the length of each leg.
\\( \frac { y } { 2 } \\)
\\( \sqrt { 2 } y \\)
\\( \frac { \sqrt { 2 } y } { 2 } \\)
\\( \sqrt { 2 y } \\)
\\( y \\)

Explanation:

Step1: Recall the ratio of sides in a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle

In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, if the length of each leg is \(a\) and the hypotenuse is \(c\), then \(c = a\sqrt{2}\).

Step2: Solve for \(a\) when \(c = 2y\)

Given \(c=2y\) and \(c = a\sqrt{2}\), we can solve for \(a\) by the equation \(a=\frac{c}{\sqrt{2}}\). Substitute \(c = 2y\) into the formula: \(a=\frac{2y}{\sqrt{2}}\). Rationalize the denominator: \(a=\frac{2y\sqrt{2}}{2}=\sqrt{2}y\).

Answer:

\(\sqrt{2}y\)