Question

What is the length of the hypotenuse of a right triangle with sides that measure 7 cm and 24 cm?

Answer 1

The length of the hypotenuse of a right triangle with sides that measure 7 cm and 24 cm is 25 cm

Solution:

Given a right angled triangle,

The sides measure 7 cm and 24 cm

We have to find the length of hypotenuse

For a right angled triangle, by Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

From above definition we get,

`c^2 = a^2 + b^2`

Where, "c" is the length of hypotenuse

"a" is the length of one side of triangle

"b" is the length of other side of triangle

Here, a = 7 and b = 24 and c = ?

`c^2 = 7^2 + 24^2\\\\c^2 = 49 + 576 = 625`

Taking square root on both sides,

`c = √(625)\\\\c = 25`

Hence the length of hypotenuse is 25 cm