the two legs of a right angled triangle are equal in length and the square of the length of its hypotenuse is 72cm find the length of each leg.
2x^2 = 72
x = 6
note: the square on the hypotenuse is 72 cm^2
To find the lengths of the legs of a right-angled triangle, we can solve the problem using the Pythagorean theorem.
Let's denote the length of each leg as "x."
According to the problem, the two legs are equal in length, so we have:
Length of leg 1 = x
Length of leg 2 = x
Now, using the Pythagorean theorem, we know that:
Hypotenuse^2 = Leg 1^2 + Leg 2^2
Substituting the values, we get:
72cm = x^2 + x^2
Combine like terms:
72cm = 2x^2
Divide both sides of the equation by 2:
36cm = x^2
Now, we need to find the square root of both sides to isolate "x":
√(36cm) = √(x^2)
6cm = x
So, the length of each leg of the right-angled triangle is 6 cm.