To find the length of the hypotenuse of a right triangle when we know the lengths of the two legs, we can use the Pythagorean theorem. The Pythagorean theorem states:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the lengths of the legs, and [tex]\( c \)[/tex] is the length of the hypotenuse.
Given:
- The length of the first leg ([tex]\( a \)[/tex]) is 36 units.
- The length of the second leg ([tex]\( b \)[/tex]) is also 36 units.
We need to find:
- The length of the hypotenuse ([tex]\( c \)[/tex]).
Step-by-step solution:
1. Write down the Pythagorean theorem:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
2. Substitute the given lengths of the legs into the equation:
[tex]\[ 36^2 + 36^2 = c^2 \][/tex]
3. Calculate the squares:
[tex]\[ 1296 + 1296 = c^2 \][/tex]
4. Add these values:
[tex]\[ 2592 = c^2 \][/tex]
5. Solve for [tex]\( c \)[/tex] by taking the square root of both sides:
[tex]\[ c = \sqrt{2592} \][/tex]
6. Simplify the square root:
[tex]\[ c = 50.91168824543142 \][/tex] units
Therefore, the length of the hypotenuse of the triangle DEF is approximately 50.91168824543142 units.
