Question

a right triangle and two of its side lengths are shown in the diagram. 12 cm 39 cm x cm which measurement is closest to the value of x in centimeters? a 27 cm b 37.1 cm c 51 cm d 40.8 cm

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, $c = 39$ cm, $a = 12$ cm, and $b=x$. So, $x=\sqrt{39^{2}-12^{2}}$.

Step2: Calculate squares

$39^{2}=39\times39 = 1521$ and $12^{2}=12\times12 = 144$. Then $39^{2}-12^{2}=1521 - 144=1377$.

Step3: Find square - root

$x=\sqrt{1377}\approx37.1$ cm.

Answer:

B. 37.1 cm