The length of one leg of an isosceles right triangle is 3 ft. What is the perimeter of the triangle?
3 + 3 StartRoot 2 EndRoot ft
3 + 3 StartRoot 3 EndRoot ft
6 + 3 StartRoot 2 EndRoot ft
6 + 3 StartRoot 3 EndRoot ft

The perimeter of the isosceles right triangle is P = 6 + 3√2 feet

A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle

The three types of Isosceles Triangles are :

Isosceles acute triangle

Isosceles right triangle

Isosceles obtuse triangle

Given data ,

Let the isosceles triangle be represented as ΔABC

In an isosceles right triangle, the two legs are congruent, so if one leg has a length of 3 ft, then the other leg also has a length of 3 ft. Let's call the length of the hypotenuse h.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

h² = 3² + 3²

h² = 18

Taking square roots on both sides , we get

h = 3√2 feet

The perimeter of the triangle is the sum of the lengths of its sides:

Perimeter = 3 + 3 + 3√2 = 6 + 6 + 3√2 feet

Hence , the perimeter is 6 + 3√2 feet

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