Question 8 of 25

The hypotenuse of a 45-45-90 triangle has a length of 10 units. What is the length of one of its legs?

A. [tex]5 \sqrt{2}[/tex] units
B. [tex]10 \sqrt{2}[/tex] units
C. 10 units
D. 5 units



Answer :

To solve for the length of one of the legs in a 45-45-90 triangle where the hypotenuse is 10 units, we can follow these steps:

1. Understand the properties of a 45-45-90 triangle:
- In a 45-45-90 triangle, the two legs are of equal length.
- The relationship between the hypotenuse (h) and each leg (x) is given by the formula:
[tex]\[ h = x \sqrt{2} \][/tex]
2. Substitute the known value into the formula:
- We are given the hypotenuse [tex]\( h = 10 \)[/tex] units.
- Substitute [tex]\( h \)[/tex] into the equation:
[tex]\[ 10 = x \sqrt{2} \][/tex]

3. Solve for [tex]\( x \)[/tex]:
- To isolate [tex]\( x \)[/tex], divide both sides of the equation by [tex]\( \sqrt{2} \)[/tex]:
[tex]\[ x = \frac{10}{\sqrt{2}} \][/tex]

4. Simplify the expression:
- Rationalize the denominator by multiplying the numerator and the denominator by [tex]\( \sqrt{2} \)[/tex]:
[tex]\[ x = \frac{10 \sqrt{2}}{2} \][/tex]
- Simplify the fraction:
[tex]\[ x = 5 \sqrt{2} \][/tex]

Therefore, the length of one of the legs of the triangle is [tex]\( 5 \sqrt{2} \)[/tex] units.

Thus, the correct answer is:

A. [tex]\( 5 \sqrt{2} \)[/tex] units