Quadratic Area Problem

The area of a playground is 504 square yards.  The length of the playground is (x +8) and the width is (x – 2).  Find the length and width.

• 20

• -26 and 20

• 18 and 28

• 14 and 36

The length of a tropical garden at a conservatory is 5 feet more than its width.  A walkway 2 feet wide surrounds the outside of the garden.  If the total area of the walkway and garden is 126 square feet, find the dimensions of the garden.

• 2(x+2) + 2(x+7) = 126

• 2(x+4) + 2(x+ 9) = 126

• (x+2)(x+9) = 126

• (x+4)(x+11) = 126

The width of a rectangle is 8 meters less than its length. If the area of the rectangle is 84 m², find the dimensions of the rectangle.

• x(x-8)=84

• x(x-4)=84

• x(x+8)=84

• x(x-8)=168

The area of a rectangle is 96 feet squared. The length of the rectangle is (x-4) feet and the width is (x) feet. Find the value of x.

• 12 feet

• 8 feet

• 6 feet

• 16 feet

Solve x²+2x=24 for x.

• x=-4 or x=6

• x=4 or x=-6

• x=0 or x=-2

• x=11 or x=-11

The length of a rectangle is 2 units more than the height.

Given the total area is 80, which equation is correct

• x(x+2) = 80

• x(x+2) = 40

• x+(x+2) = 80

• 2(x+(x+2)) = 80

A rectangular photograph measuring 6 cm by 4 cm is to be displayed in a card mount in a rectangular frame, as shown in the diagram.

Which of the following equations can be used to find 𝑥 if the area of the mount is 64 cm²?

• (4+2𝑥)(6+2𝑥)−24=64

• (3+2𝑥)(6−5𝑥)−21=32

• (7+2𝑥)(5+2𝑥)−13=64

• (9+5𝑥)(3+7𝑥)−15=18

• (5+2𝑥)(7−2𝑥)−24=28

The diagram shows the floor plan of a building.

The total area is 24.

This leads to the equation x²+x-a=0

Find the value of a

The diagram shows the floor plan of a building.

The total area is 24.

This leads to the equation x²+x-6=0

Find the value of x

What quadratics does this diagram represent?

Mathematical Equivalence

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