An isosceles right triangle has a hypotenuse of 18m. Find the other two sides?
Pythagorean theorem.
s^2 + s^2 = 2s^2 = 18^2
Solve for s.
To find the other two sides of an isosceles right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that 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.
In an isosceles right triangle, since it is isosceles, the two legs are of equal length. Let's call the length of each leg "x."
According to the Pythagorean theorem, we can write the equation as:
x^2 + x^2 = 18^2
Simplifying this equation, we have:
2x^2 = 324
Dividing both sides of the equation by 2, we get:
x^2 = 162
To find the value of x, we take the square root of both sides of the equation:
x = √162
Simplifying the square root of 162, we get:
x ≈ 12.73
So, the length of each leg in the isosceles right triangle is approximately 12.73 meters.
To find the lengths of the other two sides of an isosceles right triangle, we need to use the Pythagorean theorem.
In an isosceles right triangle, the two legs (the two sides that are not the hypotenuse) are congruent.
Let's assume that the length of both legs is 'x'. Therefore, we can write the Pythagorean theorem equation as:
x^2 + x^2 = 18^2
Simplifying the equation, we have:
2x^2 = 324
Divide both sides of the equation by 2:
x^2 = 162
To find the value of 'x', we need to take the square root of both sides:
x = sqrt(162)
Taking the square root, we get:
x ≈ 12.73
Therefore, the lengths of the other two sides of the isosceles right triangle are approximately 12.73 meters each.