Question

what is the perimeter? if necessary, round to the nearest tenth. kilometers

Explanation:

Step1: Find the length of the hypotenuse \(c\) using the Pythagorean theorem

For a right - triangle with legs \(a = 24\) and \(b=45\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\).
Substitute \(a = 24\) and \(b = 45\) into the formula:
\(c^{2}=24^{2}+45^{2}=576 + 2025=2601\)
Take the square root of both sides: \(c=\sqrt{2601}=51\)

Step2: Calculate the perimeter \(P\) of the triangle

The perimeter of a triangle is \(P=a + b + c\).
Substitute \(a = 24\), \(b = 45\), and \(c = 51\) into the formula:
\(P=24+45 + 51=120\)

Answer:

\(120\)