Answer :
To determine the length of one leg of a 45°-45°-90° triangle when the hypotenuse measures \( 22 \sqrt{2} \) units, follow these steps:
1. Understand the Properties of a 45°-45°-90° Triangle:
- In a 45°-45°-90° triangle, the sides are in a specific ratio. If each leg is of length \( x \), the hypotenuse will be \( x\sqrt{2} \). This is because the legs are congruent (equal) and the hypotenuse is found using the Pythagorean theorem: \( (leg)^2 + (leg)^2 = (hypotenuse)^2 \).
2. Set Up the Ratios:
- Let the length of one leg be \( x \). Then, according to the properties of the triangle:
[tex]\[ \text{Hypotenuse} = x \sqrt{2} \][/tex]
- We are given that the hypotenuse is \( 22 \sqrt{2} \).
3. Solve for \( x \):
- Replace the hypotenuse in the equation with the given value:
[tex]\[ 22 \sqrt{2} = x \sqrt{2} \][/tex]
- Divide both sides by \( \sqrt{2} \) to isolate \( x \):
[tex]\[ x = \frac{22 \sqrt{2}}{\sqrt{2}} \][/tex]
- Simplify the expression. Since \( \sqrt{2} \) in the numerator and denominator cancels out:
[tex]\[ x = 22 \][/tex]
4. Conclusion:
- The length of one leg of the triangle is [tex]\( \boxed{22 \text{ units}} \)[/tex].
1. Understand the Properties of a 45°-45°-90° Triangle:
- In a 45°-45°-90° triangle, the sides are in a specific ratio. If each leg is of length \( x \), the hypotenuse will be \( x\sqrt{2} \). This is because the legs are congruent (equal) and the hypotenuse is found using the Pythagorean theorem: \( (leg)^2 + (leg)^2 = (hypotenuse)^2 \).
2. Set Up the Ratios:
- Let the length of one leg be \( x \). Then, according to the properties of the triangle:
[tex]\[ \text{Hypotenuse} = x \sqrt{2} \][/tex]
- We are given that the hypotenuse is \( 22 \sqrt{2} \).
3. Solve for \( x \):
- Replace the hypotenuse in the equation with the given value:
[tex]\[ 22 \sqrt{2} = x \sqrt{2} \][/tex]
- Divide both sides by \( \sqrt{2} \) to isolate \( x \):
[tex]\[ x = \frac{22 \sqrt{2}}{\sqrt{2}} \][/tex]
- Simplify the expression. Since \( \sqrt{2} \) in the numerator and denominator cancels out:
[tex]\[ x = 22 \][/tex]
4. Conclusion:
- The length of one leg of the triangle is [tex]\( \boxed{22 \text{ units}} \)[/tex].
