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.

This can be solved with the Pythagorean Theorem.  

6² + 4² = c²

52 = c²

c = √52 = 2√13

By drawing Angela’s route, we can connect her end point and her start point with a straight line and will then have a right triangle. The Pythagorean theorem can be used to solve for how far she is from the starting point: a²+b²=c², 30²+40²=c², c=50. It can also be noted that Angela’s route represents a multiple of the 3-4-5 Pythagorean triple.

Since east and north directions are perpendicular, the possible routes Bob can take can be represented by a right triangle with sides a and b of length 3 miles and 5 miles, respectively. The hypotenuse c represents the straight line connecting his house to the store, and its length can be found using the Pythagorean theorem: c² = 3²+ 4² = 25. Since the square root of 25 is 5, the length of the hypotenuse is 5 miles.

This question requires the use of Pythagorean Theorem. We are given the length of two sides of a triangle and asked to find the third. We are told that the two sides we are given meet at a right angle, this means that the missing side is the hypotenuse. So we use a² + b² = c², plugging in the two known lengths for a and b. This yields an answer of 27.46 feet.

Kathy's path traces the outline of a right triangle with legs of 6 and 8. By using the Pythagorean Theorem

miles