Question

The two legs of a right triangle are 6 feet and 8feet long. what is the perimeter of the triangle?

Answer 1

Hello from MrBillDoesMath!

Answer:

24

Discussion:

In a right triangle with legs 6, and 8, by the Pythagorean theorem the hypotenuse is sqrt( 6^2 + 8^2) = sqrt (36 + 64) = sqrt(100) = 10.

The perimeter is the sum of the side (and hypotenuse) lengths:

Perimeter = 6 + 8 + 10 = 24

Thank you,

MrB

Answer 2

The perimeter of the right triangle is 24 feet.

Given the following data;

• Adjacent = 6 feet

• Opposite = 8 feet

To find the perimeter of the right triangle;

Mathematically, the perimeter of a right triangle is given by the formula;

`P = A + B + C`

But we were only given two (2) of its sides or legs, so we would have to solve for the third side (hypotenuse) by using the Pythagorean theorem.

`C^(2) = A^(2) + B^(2)`

Where;

C is the hypotenuse of a right triangle.

A is the opposite side of a right triangle.

B is the adjacent side of a right triangle.

Substituting the values

`C^(2) = 8^(2) + 6^(2)\\\\C^(2) = 64 + 36\\\\C^(2) = 100`

Taking the square root of both sides, we have;

`C = √(100)`

Hypotenuse, C = 10 feet.

Next, we find the perimeter of the right triangle;

`P = 8 + 6 + 10`

Perimeter, P = 24 feet.

Therefore, the perimeter of the right triangle is 24 feet.

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