Pythagorean Theorem Applications

The video tutorial explores application problems using the Pythagorean theorem. It begins with a scenario where Peter runs a path forming a right triangle, calculating the diagonal distance. Next, it addresses a problem involving caution tape across a barn door, using the theorem to find the tape length. Finally, it examines squares on the legs and hypotenuse of a right triangle, calculating areas and perimeters.

What is the first step in solving Peter's journey problem using the Pythagorean theorem?

• Find the area of the triangle.

• Subtract the distances.

• Draw a picture to visualize the problem.

• Calculate the total distance traveled.

How do you calculate the diagonal distance Peter ran?

• Add the distances traveled east and north.

• Multiply the distances traveled east and north.

• Subtract the distances traveled east and north.

• Use the Pythagorean theorem: 3 squared plus 4 squared equals c squared.

How much shorter is the diagonal path compared to the path Peter took?

• 1 mile

• 2 miles

• 3 miles

• 4 miles

What shape does the caution tape form on the barn door?

• A square

• An X

• A rectangle

• A triangle

How do you calculate the length of one piece of caution tape?

• Add the length and width of the door.

• Use the Pythagorean theorem: 10 squared plus 4 squared equals c squared.

• Multiply the length and width of the door.

• Subtract the width from the length of the door.

What is the total length of caution tape needed for both diagonals?

• 10.8 feet

• 15.6 feet

• 25.6 feet

• 21.6 feet

What does the area of square one represent in the final example?

• The perimeter of the triangle

• The hypotenuse squared

• The difference between the legs

• The sum of the legs

How do you find the side length of square two?

• Multiply the perimeter by four

• Subtract the area from the perimeter

• Add the perimeter to the area

• Divide the perimeter by four

What is the area of square three?

• 36 square inches

• 64 square inches

• 100 square inches

• 128 square inches

What is the relationship between the areas of the squares in the final example?

• The area of square three is the sum of the areas of squares one and two.

• The area of square two is the sum of the areas of squares one and three.

• The area of square one is the difference between the areas of squares two and three.

• The area of square one is the sum of the areas of squares two and three.