The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or  angle. When a triangle includes a right angle, the triangle is said to be a "right triangle." 

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or  angle. When a triangle includes a right angle, the triangle is said to be a "right triangle." 

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or  angle. When a triangle includes a right angle, the triangle is said to be a "right triangle." 

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

or

The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or  angle. When a triangle includes a right angle, the triangle is said to be a "right triangle." 

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

or

The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or  angle. When a triangle includes a right angle, the triangle is said to be a "right triangle." 

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

By the  Theorem:

, and

The perimeter of the parallelogram is

Given that a rectangle has all right angles, drawing a diagonal will create a right triangle the legs are each 6 feet and 8 feet. 

We know that in a 3-4-5 right triangle, when the legs are 3 feet and 4 feet, the hypotenuse will be 5 feet. 

Given that the legs of this triangle are twice as long as those in the 3-4-5 triangle, it follows that the hypotense will also be twice as long. 

Thus, the diagonal in through the rectangle creates a 6-8-10 triangle. 10 is therefore the length of the diagonal. 

This problem is solved using the Pythagorean theorem  .  In this formula  and  are the legs of the right triangle while  is the hypotenuse.

Using the labels of our triangle we have:

Sam and John have walked at right angles to each other, so the distance between them is the hypotenuse of a triangle.  The distance can be found using the Pythagorean Theorem.

First let's calculate how far Daria walks. This is simply 1 mile north + 1 mile east = 2 miles. Now let's calculate how far Ashley walks. We can think of this problem using a right triangle. The two legs of the triangle are the 1 mile north and 1 mile east, and Ashley's distance is the diagonal. Using the Pythagorean Theorem we calculate the diagonal as √(1² + 1²) = √2. So Daria walked 2 miles, and Ashley walked √2 miles. Therefore the difference is simply 2 – √2 miles.