Question

one leg of a right triangle has a length of 7 m. the other sides have lengths that are consecutive integers. find these lengths. the other leg is 24 m. the length of the hypotenuse is (square) m.

Explanation:

Step1: Apply Pythagorean theorem

Let the other leg be \(a = 24\) m and the hypotenuse be \(c\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(b = 7\) m.

Step2: Substitute values

Substitute \(a = 24\) and \(b = 7\) into the formula: \(24^{2}+7^{2}=c^{2}\).
Calculate \(24^{2}=576\) and \(7^{2}=49\). Then \(576 + 49=c^{2}\), so \(c^{2}=625\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{625}\).

Answer:

\(25\)