Area Problems Quadratic Equations

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 area of a playground is 336 yd2 . The width of the playground is 5 yd longer than its length. Find the length and width of the playground

•  length = 26 yd, width = 21 yd

• length = 21 yd, width = 26 yd 

• length = 21 yd, width = 16 yd 

• length = 16 yd, width = 21 yd

The length of a rectangular parking is 9m longer than its width and the area of the lot is 36m². How will you represent the length of the parking lot?

• x

• x + 36

• x + 9

• x - y

Answer to part c is....

Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation: h = -16t^2 + 80 About how long did it take for the balloon to hit the ground?

• 1.73 seconds

• 2.24 seconds

• 2.45 seconds

• 2.83 seconds

The length of a rectangle is 7 inches more than its width, its area is 228 square inches. Determine the length of the given rectangle.

• 18 m

• 19 m

• 20 m

• 21 m

The area of a carpet is 144 sq. meters. Its length is 2 meters more than its width. Represent the length using a variable.

• x - 144

• x + 144

• x - 2

• x + 2

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

Given the perimeter is 80, find the length of the rectangle.

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