Question

the legs of a right triangle are 30 cm and 72 cm. find the length of the hypotenuse.

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 30\) cm and \(b=72\) cm. The Pythagorean theorem for a right - triangle is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse.
So \(c^{2}=30^{2}+72^{2}\).

Step2: Calculate squares

\(30^{2}=30\times30 = 900\) and \(72^{2}=72\times72=5184\). Then \(a^{2}+b^{2}=900 + 5184=6084\).

Step3: Find square - root

\(c=\sqrt{6084}\). Since \(78\times78 = 6084\), \(c = 78\) cm.

Answer:

78 cm