Question

find the length of the leg. if your answer is not an integer, leave it in simplest radical form.

14

7√2

√7

98

Explanation:

Step1: Use the property of a 45 - 45 - 90 triangle

In a 45 - 45 - 90 triangle, the ratio of the sides is \(1:1:\sqrt{2}\). Let the length of each leg be \(x\). The hypotenuse \(c\) is related to the leg \(x\) by the formula \(c = x\sqrt{2}\). Given \(c = 14\).

Step2: Solve for \(x\)

We have \(14=x\sqrt{2}\). Then \(x=\frac{14}{\sqrt{2}}\). Rationalize the denominator: \(x=\frac{14\sqrt{2}}{2}=7\sqrt{2}\).

Answer:

\(7\sqrt{2}\) (corresponding to the second option \(7\sqrt{2}\))