Answer :
To determine the length of the hypotenuse in an isosceles right triangle where the legs each have a length of \( 15 \sqrt{2} \) feet, we will follow these steps:
1. Understand the properties of an isosceles right triangle:
- In an isosceles right triangle, the two legs are of equal length.
- The hypotenuse is opposite the right angle.
- In such triangles, the relationship between the leg lengths and the hypotenuse is given by the Pythagorean theorem.
2. Apply the formula for the hypotenuse in an isosceles right triangle:
- For an isosceles right triangle with legs of length \( a \), the hypotenuse \( c \) can be found using the formula:
[tex]\[ c = a \sqrt{2} \][/tex]
- Here, each leg \( a \) is given as \( 15 \sqrt{2} \).
3. Substitute the given leg length into the hypotenuse formula:
- Leg length \( a = 15 \sqrt{2} \).
- Therefore, the hypotenuse \( c \) is:
[tex]\[ c = 15 \sqrt{2} \times \sqrt{2} \][/tex]
4. Simplify the expression:
- Notice that \(\sqrt{2} \times \sqrt{2} = 2\). Therefore:
[tex]\[ c = 15 \sqrt{2} \times 2 \][/tex]
- Simplify the multiplication:
[tex]\[ c = 30 \][/tex]
5. Conclusion:
- The length of the hypotenuse is 30 feet.
Thus, the correct answer is:
[tex]\[ \boxed{30} \text{ feet} \][/tex]
1. Understand the properties of an isosceles right triangle:
- In an isosceles right triangle, the two legs are of equal length.
- The hypotenuse is opposite the right angle.
- In such triangles, the relationship between the leg lengths and the hypotenuse is given by the Pythagorean theorem.
2. Apply the formula for the hypotenuse in an isosceles right triangle:
- For an isosceles right triangle with legs of length \( a \), the hypotenuse \( c \) can be found using the formula:
[tex]\[ c = a \sqrt{2} \][/tex]
- Here, each leg \( a \) is given as \( 15 \sqrt{2} \).
3. Substitute the given leg length into the hypotenuse formula:
- Leg length \( a = 15 \sqrt{2} \).
- Therefore, the hypotenuse \( c \) is:
[tex]\[ c = 15 \sqrt{2} \times \sqrt{2} \][/tex]
4. Simplify the expression:
- Notice that \(\sqrt{2} \times \sqrt{2} = 2\). Therefore:
[tex]\[ c = 15 \sqrt{2} \times 2 \][/tex]
- Simplify the multiplication:
[tex]\[ c = 30 \][/tex]
5. Conclusion:
- The length of the hypotenuse is 30 feet.
Thus, the correct answer is:
[tex]\[ \boxed{30} \text{ feet} \][/tex]
