Question

The length of one leg of an isosceles right triangle is 3 ft. What is the perimeter of the triangle?

A 3 + 3 StartRoot 2 EndRoot ft
B 3 + 3 StartRoot 3 EndRoot ft
C 6 + 3 StartRoot 2 EndRoot ft
D 6 + 3 StartRoot 3 EndRoot ft

Answer 1

its c

Explanation:

Answer 2

C.
`Perimeter = 6 + 3√(2)` ft

Explanation:

Given

The length of one side of the triangle = 3 ft

Required

The perimeter

Given that the perimeter is an isosceles right triangle, this means that two sides (the opposite and adjacent) are actually equal while the hypothenus is longer.

So, we can easily assume that

Opposite = 3 ft

Adjacent = 3 ft

then we solve for the hypothenus of the triangle

Using Pythagoras theorem

`Hyp^2 = Opp^2 + Adj^2`

Substitute 3 for opposite and adjacent

`Hyp^2 = 3^2 + 3^2`

`Hyp^2 = 2(3^2)`

Take square root of both sides

`Hyp = √(2(3^2))`

Split the surd

`Hyp = √(2) * √(3^2)`

`Hyp = √(2) * √(9)`

`Hyp = √(2) * 3`

`Hyp = 3√(2)`

Now that we have the three sides of the triangle, the perimeter is calculated by adding the values of the three sides

Perimeter = Opposite + Adjacent + Hypothenus

`Perimeter = 3 + 3 + 3√(2)`

`Perimeter = 6 + 3√(2)`

Hence, the perimeter of the triangle is
`6 + 3√(2)` ft