Question

if a ( 45^{circ}-45^{circ}-90^{circ} ) triangle has a hypotenuse length of ( 7 sqrt{2} ), what is the length of each leg of the triangle? select the correct answer. ( 7 sqrt{2} ) ( 7 ) ( sqrt{2} ) ( 2 )

Explanation:

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

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

Step2: Solve for \(a\)

Given \(c=7\sqrt{2}\), from \(c = a\sqrt{2}\), we can solve for \(a\) by dividing both sides of the equation by \(\sqrt{2}\). So \(a=\frac{7\sqrt{2}}{\sqrt{2}}\).
Simplify \(\frac{7\sqrt{2}}{\sqrt{2}}\), the \(\sqrt{2}\) terms cancel out, and we get \(a = 7\).

Answer:

B. \(7\)