Question

pythagorean unit practice
the diagram shows a right triangle and the lengths of two of its sides in inches.
which measurement is closest to the value of d in inches?
14.3 in.
6.3 in.
19.8 in.
4.0 in.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\). Here \(a = 11.9\) and \(b = 7.9\), and \(d\) is the hypotenuse. So \(d^{2}=11.9^{2}+7.9^{2}\).

Step2: Calculate squares

\(11.9^{2}=11.9\times11.9 = 141.61\) and \(7.9^{2}=7.9\times7.9 = 62.41\). Then \(d^{2}=141.61 + 62.41=204.02\).

Step3: Find \(d\)

\(d=\sqrt{204.02}\approx14.3\).

Answer:

14.3 in.