Area Problems Quadratics

The length of a rectangle is 5 inches more than twice a number. The width is 4 inches less than the same number. If the area of the rectangle is 15, find the number.

A school is building a rectangular soccer field that has an area of 6000 square yards. The soccer field must be 40 yards longer than its width. Determine the length.

• 600

• 60

• 10

• 100

A rectangle has a width that is 3cm less than the length. The area of the rectangle is 40cm². Write an equation that can be used to solve for the dimensions of the rectangle.

• (3-L)(L) = 40

• (L-3)(L) = 40

• (L+3)(L) = 40

• (-L)(L-3) = 40

A picture frame has a length which is 8 cm more than width. The area enclosed by the picture frame is 65 square cm. Find the width of the picture frame.

• 5 cm

• 8 cm

• 21 cm

• 13 cm

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 Area of a rectangle is 216 in². The length of the rectangle can be represented by 2x +10 and its width can be represented by 3x. What are the dimensions of this rectangle in inches? (Hint: Solve for x then substitute it back into the expressions for length and width!)

• Length = 12, Width = 18

• Length = 24, Width = 9

• Length = 8, Width = 27

• Length = 18, Width = 12

Edit

A rectangle has a width that is 3cm less than the length. The area of the rectangle is 40cm². Find the length and width of the rectangle

• Length = 10, Width = 4

• Length = 7, Width = 4

• Length = 5, Width = 8

• Length = 8, Width = 5

If you have 50 meters to fence in the area, write an equation to solve for the value of x that will give the maximum area.