Triangle Dimensions and Quadratic Solutions

This video tutorial explains how to solve a problem involving a right triangle using the Pythagorean theorem and a quadratic equation. The problem states that the shorter leg is seven inches shorter than the longer leg, and the hypotenuse is seven inches longer than the longer leg. The tutorial guides through setting up the equation, solving it, and verifying the solution to find the lengths of the triangle's sides.

What is the relationship between the shorter leg and the longer leg of the triangle?

• The shorter leg is equal to the longer leg.

• The shorter leg is twice the length of the longer leg.

• The shorter leg is 7 inches shorter than the longer leg.

• The shorter leg is 7 inches longer than the longer leg.

How is the hypotenuse related to the longer leg of the triangle?

• The hypotenuse is twice the length of the longer leg.

• The hypotenuse is 7 inches shorter than the longer leg.

• The hypotenuse is equal to the longer leg.

• The hypotenuse is 7 inches longer than the longer leg.

If the longer leg is represented by X, how would you express the shorter leg?

• 2X

• X

• X - 7

• X + 7

What equation represents the Pythagorean theorem for this triangle?

• a^2 + b^2 = c^2

• a^2 + b^2 = c

• a + b^2 = c^2

• a^2 + b = c^2

What is the expression for the hypotenuse in terms of X?

• X + 7

• 2X

• X - 7

• X

What is the purpose of using the Pythagorean theorem in this problem?

• To find the side lengths of the triangle.

• To find the angles of the triangle.

• To find the perimeter of the triangle.

• To find the area of the triangle.

What is the result of expanding (X - 7)^2?

• X^2 - 14X + 49

• X^2 + 14X + 49

• X^2 - 7X + 49

• X^2 + 7X + 49

What is the result of expanding (X + 7)^2?

• X^2 + 7X + 49

• X^2 - 14X + 49

• X^2 + 14X + 49

• X^2 - 7X + 49

What does the expression X^2 + 14X + 49 represent in the context of this problem?

• The area of the triangle.

• The expanded form of (X + 7)^2.

• The expanded form of (X - 7)^2.

• The perimeter of the triangle.

What is the simplified form of the quadratic equation derived from the problem?

• X^2 - 14X = 0

• X^2 + 28X = 0

• X^2 + 14X = 0

• X^2 - 28X = 0