Question

the length of one leg of an isosceles right - triangle is 3 ft. what is the perimeter of the triangle?
3 + 3\sqrt{3}ft
6 + 3\sqrt{2}ft
3 + 3\sqrt{2}ft
6 + 3\sqrt{3}ft

Explanation:

Step1: Identify side - lengths of the isosceles right - triangle

In an isosceles right - triangle, the two legs are of equal length. Given one leg is 3 ft, the other leg is also 3 ft.

Step2: Calculate the hypotenuse length

By the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\), where \(a = b=3\) ft. So \(c=\sqrt{3^{2}+3^{2}}=\sqrt{9 + 9}=\sqrt{18}=3\sqrt{2}\) ft.

Step3: Calculate the perimeter

The perimeter \(P=a + b + c\), substituting \(a = 3\), \(b = 3\) and \(c = 3\sqrt{2}\), we get \(P=3+3 + 3\sqrt{2}=6 + 3\sqrt{2}\) ft.

Answer:

\(6 + 3\sqrt{2}\text{ ft}\)