Please help me with the following by checking my answer.
The length of the hypotenuse of an isosceles right triangle is √6 inches. How long, in inches, are the legs of the triangle?
A. 3
B. 6
C. √3 - (This is my answer.)
D. √6
I am not sure on my answer, please check it to see if I am correct. Any help will be greatly appreciated. :)
correct
since the legs are hypotenuse/√2, √6/√2 = √3
check:
√3^2 + √3^2 = √6^2
3 + 3 = 6
Thank you, Steve! I really appreciate it. :)
To find the lengths of the legs of an isosceles right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the length of the legs of the isosceles right triangle as x. So, we have:
x^2 + x^2 = (√6)^2
Simplifying the equation, we get:
2x^2 = 6
Dividing both sides by 2, we get:
x^2 = 3
Taking the square root of both sides, we have:
x = √3
So, the length of each leg is √3 inches.
Therefore, your original answer is correct. The correct answer is C. √3.