The hypotenuse of a [tex][tex]$45^{\circ}-45^{\circ}-90^{\circ}$[/tex][/tex] triangle measures [tex][tex]$22 \sqrt{2}$[/tex][/tex] units.

What is the length of one leg of the triangle?

A. 11 units
B. [tex][tex]$11 \sqrt{2}$[/tex][/tex] units
C. 22 units
D. [tex][tex]$22 \sqrt{2}$[/tex][/tex] units



Answer :

To find the length of one leg of a 45°-45°-90° triangle when the hypotenuse is given, it's important to understand the special properties of this type of triangle. In a 45°-45°-90° triangle, the legs are equal in length, and the hypotenuse is [tex]\(\sqrt{2}\)[/tex] times the length of one leg.

Given that the hypotenuse measures [tex]\(22 \sqrt{2}\)[/tex] units, we can use this relationship to determine the length of one leg.

1. Let [tex]\(x\)[/tex] be the length of one leg of the triangle.
2. According to the properties of a 45°-45°-90° triangle, the hypotenuse [tex]\(c\)[/tex] is related to the leg [tex]\(x\)[/tex] by the formula:
[tex]\[ c = x \sqrt{2} \][/tex]

3. Plugging in the given hypotenuse value:
[tex]\[ 22 \sqrt{2} = x \sqrt{2} \][/tex]

4. To isolate [tex]\(x\)[/tex], divide both sides of the equation by [tex]\(\sqrt{2}\)[/tex]:
[tex]\[ x = \frac{22 \sqrt{2}}{\sqrt{2}} \][/tex]

5. Simplifying the fraction on the right-hand side, [tex]\(\sqrt{2}\)[/tex] cancels out:
[tex]\[ x = 22 \][/tex]

So, the length of one leg of the triangle is [tex]\(22\)[/tex] units.

Therefore, the correct answer is:
22 units