The legs of a right-angled triangle are 18 and 24. find the hypotenuse.

From the condition we know the lengths of the legs of a right triangle are 18 and 24. We need to find the hypotenuse of a right triangle.

To do this, we apply the Pythagorean theorem, which says that the square of the hypotenuse is equal to the sum of the squares of the legs.

a ^ 2 + b ^ 2 = c ^ 2;

It remains for us to substitute the known values and calculate.

18 ^ 2 + 24 ^ 2 = c ^ 2;

324 + 576 = c ^ 2;

c ^ 2 = 900;

Let’s extract the square root and get (only a positive value is suitable for us):

c = √900 = √302;

c = 30.

Answer: The length of the hypotenuse is 30.