Question

what is the measure of the missing length? 42 km 15 km 18 km? a) 38 km b) 35 km c) 28 km d) 37 km

Explanation:

Step1: Apply Pythagorean theorem

Let the missing side be $x$. First, find the length of the base of the right - triangle with height 15 km. The base of the large right - triangle is $42 - 18=24$ km. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 15$ km and $b = 24$ km.

Step2: Calculate the missing side

$x=\sqrt{15^{2}+24^{2}}=\sqrt{225 + 576}=\sqrt{801}=\sqrt{9\times89}=3\sqrt{89}\approx 28$ km

Answer:

c) 28 km