Using the Pythagorean Theorem, the length of the second leg can be determined.

We are given the length of the hypotenuse and one leg.

The perimeter of the triangle is the sum of the lengths of the sides.

A right triangle with legs 6 feet and 8 feet has hypotentuse 10 feet, as this is a right triangle that confirms to the well-known Pythagorean triple 6-8-10. The perimeter is therefore  feet, or 8 yards.

We are looking for a polygon with this perimeter. Each choice is a polygon with all sides one yard long, so we want the polygon with eight sides - the regular octagon is the correct choice.

First, we need to use the Pythagorean Theorem to find the hypotenuse of the triangle.

Now, add up all three side lengths to find the perimeter of the triangle.

First, use the Pythagorean Theorem to find the length of the hypotenuse.

Substituting in  and  for  and  (the lengths of the triangle's legs), we get:

Now, add up the three sides to find the perimeter:

In order to find the perimeter  of the right triangle, we need to first find the missing length of the hypotenuse. In order to find the hypotenuse, use the Pythagorean Theorem:

, where  and  are the lengths of the legs of the triangle, and  is the length of the hypotenuse.

Substituting in our known values:

Now that we have the lengths of all sides of the right triangle, we can calculate the perimeter:

In order to find the perimeter  of the right triangle, we need to first find the missing length of the second leg. In order to find the second leg, use the Pythagorean Theorem:

, where  and  are the lengths of the legs of the triangle, and  is the length of the hypotenuse.

Substituting in our known values:

Subtracting  from each side of the equation lets us isolate the variable for which we are solving:

Now that we have the lengths of all three sides of the right triangle, we can calculate the perimeter :

In order to find the perimeter  of the right triangle, we need to first find the missing length of the hypotenuse. In order to find the length of the hypotenuse, use the Pythagorean Theorem:

, where  and  are the lengths of the legs of the triangle, and  is the length of the hypotenuse.

Substituting in our known values:

Now that we have all three sides of the right triangle, we can calculate the perimeter:

For the triangles to be similar, the dimensions of all sides must have the same ratio by dividing the 3-4-5 triangle.

The 6-8-10 triangle will have a scale factor of 2 since all dimensions are doubled the original 3-4-5 triangle.

The only correct answer that will yield similar ratios is the   triangle with a scale factor of 4 from the 3-4-5 triangle.  

The other answers will yield different ratios.

By definition, a right triangle has to have one right angle, or a  angle, and an isosceles triangle has  equal base angles and two equal side lengths. 

You may recognize these numbers as multiples of 13 and 12 (each by a factor of 3) and remember that sides of length 5, 12 and 13 make a special right triangle. So the other leg would be 15 .

If you don't remember this, you can use Pythagorean theorem: