A rectangular triangle has 26cm long hypotenuse and 10cm long cathetus. What is it's area?

To find the area of a right triangle, we use the formula: Area = 1/2 * base * height.

In a right triangle, the two sides that form the right angle are considered the base and the height. The hypotenuse is the longest side, which is opposite the right angle.

Given that the hypotenuse is 26 cm and one of the catheti (either base or height) is 10 cm, we can use the Pythagorean theorem to find the other cathetus. 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.

So, let's denote the unknown cathetus as 'a'. According to the Pythagorean theorem:

26^2 = 10^2 + a^2 676 = 100 + a^2 a^2 = 676 - 100 a^2 = 576 a = sqrt(576) a = 24 cm

Now that we have the lengths of the base and the height (10 cm and 24 cm), we can substitute these values into the formula for the area of a right triangle:

Area = 1/2 * base * height Area = 1/2 * 10 cm * 24 cm Area = 120 square cm

So, the area of the right triangle is 120 square cm.