An isosceles right triangle has a hypotenuse of 8 units. What is the length, in units, of one the legs? Round your answer to the nearest hundredth if necessary.
An isosceles triangle is a triangle having at least two congruent sides.
In a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs.
Thus, c^2 = a^2 + b^2
Therefore, since a = b, or x = x, in your problem
8^2 = x^2 + x^2
Solve this equation for x for your answer
To find the length of one of the legs of an isosceles right triangle with a known hypotenuse, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, since the triangle is isosceles, we know that both legs are equal in length. Let's denote the length of one of the legs as x.
Using the Pythagorean theorem, we can set up the equation:
x^2 + x^2 = 8^2
Simplifying this equation:
2x^2 = 64
Dividing both sides by 2:
x^2 = 32
Taking the square root of both sides to solve for x:
x = √32
Now, to round our answer to the nearest hundredth, we can use a calculator or a math tool. Evaluating √32 using a calculator, we find that √32 is approximately 5.66.
Therefore, the length of one of the legs of the isosceles right triangle is approximately 5.66 units when rounded to the nearest hundredth.