A triangle has sides of lengths 10, 24, and 26. Is it a right triangle? Explain.

Solution:

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given, the length of sides of a triangle are 10, 24 and 26.

We have to find whether the given triangle is the right triangle.

By pythagoras theorem,

\(a^{2}+b^{2}=c^{2}\)

Substituting the values

\((10)^{2}+(24)^{2}=(26)^{2}\)

By further calculation

100 + 576 = 676

LHS = RHS

Therefore, the given triangle is a right triangle.

A triangle has sides of lengths 10, 24, and 26. Is it a right triangle? Explain.

Summary:

A triangle has sides of lengths 10, 24, and 26 is a right triangle.