To solve, simply use the Pythagorean Theorem.

Recall that an isosceles right triangle has two leg lengths that are equal.

Therefore, to solve for the hypotenuse let and in the Pythagorean Theorem.

Thus,

To solve, simply use the Pythagorean Theorem.

Recall that an isosceles right triangle has two leg lengths that are equal.

Therefore, to solve for the hypotenuse let and in the Pythagorean Theorem.

Thus,

Now, this is really your standard triangle. Since it is a right triangle, you know that you have at least one -degree angle. The other two angles must each be degrees, because the triangle is isosceles.

Based on the description of your triangle, you can draw the following figure:

This is derived from your reference triangle for the triangle:

For our triangle, we could call one of the legs . We know, then:

Thus, .

The area of your triangle is:

For your data, this is:

Your right triangle is a triangle. It thus looks like this:

Now, you know that you also have a reference triangle for triangles. This is:

This means that you can set up a ratio to find . It would be:

Your triangle thus could be drawn like this:

Now, notice that you can rationalize the denominator of :

Thus, the perimeter of your figure is:

Now, this is really your standard triangle. Since it is a right triangle, you know that you have at least one -degree angle. The other two angles must each be degrees, because the triangle is isosceles.

Based on the description of your triangle, you can draw the following figure:

This is derived from your reference triangle for the triangle:

For our triangle, we could call one of the legs . We know, then:

Thus, .

The area of your triangle is:

For your data, this is:

Your right triangle is a triangle. It thus looks like this:

Now, you know that you also have a reference triangle for triangles. This is:

This means that you can set up a ratio to find . It would be:

Your triangle thus could be drawn like this:

Now, notice that you can rationalize the denominator of :

Thus, the perimeter of your figure is:

Recall that an isosceles right triangle is also a triangle. Your reference figure for such a shape is:

or

Now, you know that the area of a triangle is:

For this triangle, though, the base and height are the same. So it is:

Now, we have to be careful, given that our area contains . Let's use , for "side length":

Thus, . Now based on the reference figure above, you can easily see that your triangle is:

Therefore, your perimeter is:

Recall that an isosceles right triangle is also a triangle. Your reference figure for such a shape is:

or

Now, you know that the area of a triangle is:

For this triangle, though, the base and height are the same. So it is:

Now, we have to be careful, given that our area contains . Let's use , for "side length":

Thus, . Now based on the reference figure above, you can easily see that your triangle is:

Therefore, your perimeter is:

This is a right triangle where the rope is the hypotenuse. One leg is the radius of the circle, 5 feet. The other leg is half of the tree's height, 12 feet. We can now use the Pythagorean Theorem giving us . If then .

Remember that this is a special right triangle where the ratio of the sides is:

In this case that makes it:

Where is the length of the hypotenuse.