Quilt Area and Quadratic Concepts

The video tutorial explains how to determine the width of a uniform border around a quilt using all available fabric. It involves setting up and solving a quadratic equation derived from the area calculations of the quilt and its border. The solution is found using the quadratic formula, resulting in a border width of one foot.

What is the size of the quilt mentioned in the problem?

• 3 feet by 5 feet

• 3 feet by 6 feet

• 4 feet by 6 feet

• 5 feet by 6 feet

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

How much fabric is available for the border around the quilt?

• 24 square feet

• 18 square feet

• 20 square feet

• 22 square feet

What is the formula for the area of the outer rectangle including the border?

• (3 + x)(6 + x)

• (3 + 2x)(6 + 2x)

• (3 + x)(6 + 2x)

• (3 + 2x)(6 + x)

What is the area of the inner rectangle (the quilt itself)?

• 20 square feet

• 18 square feet

• 16 square feet

• 12 square feet

Tags

CCSS.7.EE.B.4A

What is the first step in solving the equation for the width of the border?

• Divide both sides by 2

• Add 22 to both sides

• Multiply both sides by 2

• Clear the parentheses

Tags

CCSS.HSA-REI.B.4B

What is the greatest common factor factored out from the quadratic equation?

• 3

• 2

• 1

• 4

Tags

CCSS.HSA-REI.B.4B

What are the values of a, b, and c used in the quadratic formula after factoring?

• a = 1, b = 6, c = -9

• a = 3, b = 12, c = -18

• a = 2, b = 9, c = -11

• a = 4, b = 18, c = -22

Tags

CCSS.HSA-REI.B.4B

What is the value of the square root of 169 used in the quadratic formula?

• 11

• 12

• 13

• 14

What is the positive solution for the width of the border?

• 2 feet

• 1.5 feet

• 1 foot

• 0.5 feet

Tags

CCSS.8.EE.C.7B

Why is the negative solution for the width of the border not valid?

• Because it is less than the quilt's length

• Because it is not a whole number

• Because it is a negative length

• Because it exceeds the available fabric

Tags

CCSS.8.EE.C.7B