Exploring Right Triangles and the Pythagorean Theorem

What is the length of the carpet as mentioned in the problem?

• 5 feet

• 74 feet

• 7 feet

• Square root of 74 feet

What geometric shape is formed by the carpet's dimensions?

• Square

• Circle

• Triangle

• Rectangle

What is the diagonal measurement of the carpet?

• 5 feet

• Square root of 74 feet

• 74 feet

• 7 feet

What does the diagonal of the carpet represent in the context of the right triangle?

• Base

• Height

• Hypotenuse

• Area

Which theorem is used to relate the sides of the carpet?

• Pythagorean Theorem

• Euler's Theorem

• Binomial Theorem

• Fermat's Last Theorem

What is the formula derived from applying the Pythagorean Theorem to the carpet's dimensions?

• w^2 + 7^2 = 74

• 7^2 + 74 = w^2

• w^2 + 74 = 49

• w^2 + 49 = 74

How is the value 49 derived in the equation?

• It is the square of the diagonal

• It is the square of 74

• It is the square of 7

• It is the square of the width

What is the value of w^2 after simplifying the equation?

• 74

• 49

• 24

• 25

What mathematical operation is performed to isolate w^2 in the equation?

• Division

• Multiplication

• Subtraction

• Addition

What is the width of the carpet after solving the equation?

• 5 feet

• 7 feet

• 25 feet

• 49 feet