Question

lesson 14 checkpoint
the length of one leg of a right triangle is 6 units.
what is the approximate length of the second leg if the hypotenuse is 3 times the length of the given leg?
10 units
17 units
19 units
12 units

Explanation:

Step1: Determine hypotenuse length

Given one - leg length \(a = 6\) units and hypotenuse \(c=3a\), so \(c = 3\times6=18\) units.

Step2: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are legs and \(c\) is the hypotenuse. We know \(a = 6\) and \(c = 18\), and we want to find \(b\). Rearranging the formula for \(b\) gives \(b=\sqrt{c^{2}-a^{2}}\).

Step3: Substitute values and calculate

Substitute \(a = 6\) and \(c = 18\) into the formula: \(b=\sqrt{18^{2}-6^{2}}=\sqrt{(18 + 6)(18 - 6)}=\sqrt{24\times12}=\sqrt{288}\approx17\) (since \(\sqrt{288}\approx16.97\)).

Answer:

17 units