Answer :
Certainly! Let's consider triangle DEF. In this problem, we're dealing with a right-angled triangle where both the legs are equal in length, specifically, 36 units each.
We need to find the length of the hypotenuse of this triangle.
### Step-by-Step Solution:
1. Identifying the right triangle:
- Triangle DEF is a right-angled triangle (as its legs are equal).
2. Given data:
- Length of leg 1: 36 units
- Length of leg 2: 36 units
3. Mathematical theorem to use:
- In a right-angled triangle, the relationship between the legs [tex]\(a\)[/tex] and [tex]\(b\)[/tex] and the hypotenuse [tex]\(c\)[/tex] is given by the Pythagorean theorem:
[tex]\[ c = \sqrt{a^2 + b^2} \][/tex]
4. Substitute the given lengths into the theorem:
- Here, [tex]\(a = 36\)[/tex] and [tex]\(b = 36\)[/tex].
[tex]\[ c = \sqrt{36^2 + 36^2} \][/tex]
[tex]\[ c = \sqrt{1296 + 1296} \][/tex]
[tex]\[ c = \sqrt{2592} \][/tex]
[tex]\[ c = 36 \sqrt{2} \][/tex]
5. Numerical calculation:
- The value of [tex]\(36 \sqrt{2}\)[/tex] approximately equals 50.91168824543143.
### Conclusion:
- The legs of triangle DEF are both 36 units.
- The hypotenuse of the triangle DEF is approximately 50.91168824543143 units.
Thus, the detailed step-by-step solution confirms the lengths of the legs and the hypotenuse for the right-angled triangle DEF.
We need to find the length of the hypotenuse of this triangle.
### Step-by-Step Solution:
1. Identifying the right triangle:
- Triangle DEF is a right-angled triangle (as its legs are equal).
2. Given data:
- Length of leg 1: 36 units
- Length of leg 2: 36 units
3. Mathematical theorem to use:
- In a right-angled triangle, the relationship between the legs [tex]\(a\)[/tex] and [tex]\(b\)[/tex] and the hypotenuse [tex]\(c\)[/tex] is given by the Pythagorean theorem:
[tex]\[ c = \sqrt{a^2 + b^2} \][/tex]
4. Substitute the given lengths into the theorem:
- Here, [tex]\(a = 36\)[/tex] and [tex]\(b = 36\)[/tex].
[tex]\[ c = \sqrt{36^2 + 36^2} \][/tex]
[tex]\[ c = \sqrt{1296 + 1296} \][/tex]
[tex]\[ c = \sqrt{2592} \][/tex]
[tex]\[ c = 36 \sqrt{2} \][/tex]
5. Numerical calculation:
- The value of [tex]\(36 \sqrt{2}\)[/tex] approximately equals 50.91168824543143.
### Conclusion:
- The legs of triangle DEF are both 36 units.
- The hypotenuse of the triangle DEF is approximately 50.91168824543143 units.
Thus, the detailed step-by-step solution confirms the lengths of the legs and the hypotenuse for the right-angled triangle DEF.
