Question

i) what is the length of the hypotenuse? if necessary, round to the nearest tenth.ii) c = \boxed{} meters

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, the Pythagorean theorem states that \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the lengths of the legs of the right - triangle and \(c\) is the length of the hypotenuse. Here, \(a = 2\space m\) and \(b=4\space m\). So we substitute these values into the formula: \(2^{2}+4^{2}=c^{2}\).

Step2: Calculate the left - hand side

First, calculate \(2^{2}=4\) and \(4^{2} = 16\). Then, \(2^{2}+4^{2}=4 + 16=20\). So we have the equation \(c^{2}=20\).

Step3: Solve for \(c\)

To find \(c\), we take the square root of both sides of the equation \(c^{2}=20\). So \(c=\sqrt{20}\). We can simplify \(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\approx2\times2.24 = 4.48\) (rounded to the nearest hundredth).

Answer:

\(c\approx4.48\) meters (or \(c = 2\sqrt{5}\) meters)