Question

which statement about the length of the hypotenuse of a right triangle whose legs are 7.5 inches and 8.5 inches is true? the hypotenuse is between 8 and 9 inches. the hypotenuse is between 9 and 10 inches. the hypotenuse is between 10 and 11 inches. the hypotenuse is between 11 and 12 inches.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 7.5\) inches and \(b=8.5\) inches, the length of the hypotenuse \(c\) is given by \(c=\sqrt{a^{2}+b^{2}}\). So \(c = \sqrt{7.5^{2}+8.5^{2}}=\sqrt{56.25 + 72.25}=\sqrt{128.5}\).

Step2: Estimate the value of \(\sqrt{128.5}\)

We know that \(11^{2}=121\) and \(12^{2}=144\). Since \(121<128.5<144\), then \(\sqrt{121}<\sqrt{128.5}<\sqrt{144}\), which means \(11 < \sqrt{128.5}<12\).

Answer:

The hypotenuse is between 11 and 12 inches.