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

What is the length of one leg of the triangle?

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



Answer :

In a [tex]\( 45^\circ - 45^\circ - 90^\circ \)[/tex] triangle, the properties of the triangle are well defined. Specifically, the legs of such a triangle are congruent (they have the same length), and the hypotenuse is [tex]\( \sqrt{2} \)[/tex] times the length of each leg.

Let's denote the length of each leg of the triangle as [tex]\( L \)[/tex]. According to the properties of a [tex]\( 45^\circ - 45^\circ - 90^\circ \)[/tex] triangle, the hypotenuse (H) can be expressed as:

[tex]\[ \text{H} = L \cdot \sqrt{2} \][/tex]

Given that the hypotenuse is [tex]\( 22 \sqrt{2} \)[/tex]:

[tex]\[ 22 \sqrt{2} = L \cdot \sqrt{2} \][/tex]

To find the leg length [tex]\( L \)[/tex], we can divide both sides of the equation by [tex]\( \sqrt{2} \)[/tex]:

[tex]\[ L = \frac{22 \sqrt{2}}{\sqrt{2}} \][/tex]

Since [tex]\( \sqrt{2} \)[/tex] in the numerator and denominator cancels out, we get:

[tex]\[ L = 22 \][/tex]

Therefore, the length of one leg of the triangle is [tex]\( 22 \)[/tex] units. Hence, the correct answer to the question is:

22 units