Question

Determine whether the given lengths are sides of a right triangle. Explain your reasoning. $$7,24,26$$

Short answer

The lengths 7, 24 and 26 are sides of a right triangle because the square of the longest side is equal to the sum of squares of the other two sides (\(7^2 + 24^2 = 26^2\)).

Step-by-step solution

Identification

From the given lengths, identify the longest side. Here the longest length is 26.

Apply Pythagorean theorem

Apply the Pythagorean theorem by squaring the lengths of the two shorter sides and adding them together. Also square the longest side. Calculate \(7^2 + 24^2\) and \(26^2\).

Compare the values

Compare the values obtained. If the sum of squares of the two shorter sides is equal to the square of the longest side, those lengths form a right triangle. If not, they don't form a right triangle.