If a [tex]$45^{\circ}-45^{\circ}-90^{\circ}$[/tex] triangle has a hypotenuse length of [tex]$7 \sqrt{2}$[/tex], what is the length of each leg of the triangle? Select the correct answer.

A. [tex]$7 \sqrt{2}$[/tex]
B. 7
C. [tex]$\sqrt{2}$[/tex]
D. 2



Answer :

To find the length of each leg in a [tex]\(45^\circ-45^\circ-90^\circ\)[/tex] triangle given the hypotenuse, we can use the properties of this type of triangle. In a [tex]\(45^\circ-45^\circ-90^\circ\)[/tex] triangle, both legs are of equal length, and the relationship between the lengths of the legs and the hypotenuse is such that each leg is [tex]\(\frac{1}{\sqrt{2}}\)[/tex] times the length of the hypotenuse.

Given:
Hypotenuse = [tex]\(7\sqrt{2}\)[/tex]

We want to find the length of each leg. To do that, we divide the hypotenuse by [tex]\(\sqrt{2}\)[/tex]:
[tex]\[ \text{Length of each leg} = \frac{\text{Hypotenuse}}{\sqrt{2}} \][/tex]
[tex]\[ \text{Length of each leg} = \frac{7\sqrt{2}}{\sqrt{2}} \][/tex]

Simplifying the fraction:
[tex]\[ \text{Length of each leg} = 7 \][/tex]

Therefore, the length of each leg in the triangle is 7.

The correct answer is: 7