Quadratic Area Problems

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

• A

• B

• C

• D

Answer to part c is....

Ellen has a rectangular shaped pool that is 30 feet by 18 feet. She would like to increase the length and width by the same amount, x, so the new pool is three times of the current area. Find the value of x to the nearest tenth of a foot.

• x = 15.9 ft

• x = 16.7 ft

• x = 64.7 ft

• x = 16.6 ft

The original plan for Mr. Harris’s house is a rectangle that measures 40’ x 50’. Because of an increase in cost, the square footage of the house must be decreased to 1739 square feet. To do this, the length and width will be decreased by the same amount. By how much should they be decreased?

• 6 ft

• 43.5 ft

• 3 ft

• 1.5 ft

What quadratics does this diagram represent?

Mathematical Equivalence

ON

What quadratics does this diagram represent?

Mathematical Equivalence

ON