Pythagorean Theorem Applications

The video tutorial explains how to find the lengths of the sides of a right triangle using the Pythagorean Theorem. It begins by introducing the problem, then explains the theorem, sets up the equation, and solves it step by step. The process includes factoring and verifying the solutions to ensure they make sense in the context of the problem.

What is the relationship between the lengths of the legs and the hypotenuse in the given right triangle problem?

• The hypotenuse is shorter than both legs.

• The hypotenuse is 8 meters longer than the shortest leg.

• One leg is 7 meters longer than the hypotenuse.

• Both legs are of equal length.

Which theorem is used to solve the problem of finding the side lengths of the right triangle?

• Pythagorean Theorem

• Triangle Inequality Theorem

• Sine Rule

• Cosine Rule

In the Pythagorean Theorem, what do the variables a, b, and c represent?

• a, b, and c are all the hypotenuse

• a is the hypotenuse, b and c are the legs

• a and b are the legs, c is the hypotenuse

• a and b are the hypotenuse, c is a leg

How is the equation set up using the Pythagorean Theorem for this problem?

• x^2 + x^2 = (x+7)^2

• (x+7)^2 + (x+8)^2 = x^2

• x^2 + (x+8)^2 = (x+7)^2

• x^2 + (x+7)^2 = (x+8)^2

What is the first step in solving the equation after setting it up?

• Divide both sides by x

• Multiply both sides by 2

• Expand the binomials

• Subtract 7 from both sides

What is the result of combining like terms in the equation?

• x^2 + 14x + 49 = x^2 + 16x + 64

• x^2 + 14x + 49 = 2x^2 + 16x + 64

• 2x^2 + 14x + 49 = x^2 + 16x + 64

• 3x^2 + 14x + 49 = x^2 + 16x + 64

What is the value of x after solving the quadratic equation?

• x = 7

• x = 8

• x = 5

• x = 3

What is the length of the longer leg of the triangle?

• 7 meters

• 13 meters

• 5 meters

• 12 meters

What is the length of the hypotenuse of the triangle?

• 15 meters

• 14 meters

• 13 meters

• 12 meters

Why is the solution x = -3 not applicable in this problem?

• Because x must be greater than 10

• Because x cannot be a decimal

• Because x must be an even number

• Because x must be a positive length