AREA OF RECTANGLE: Length * Width



Quadratic Equations and Area of Rectangles Sheet:

#1: Consider the situation where you want to create and fence a rectangular pen, but you only have 24 yards of fencing. What is the largest space this rectangular pen could cover?

|Length |Width |

|Uniform Width: |Maximum area for three sides: One side of the rectangle is already given like a river or |

|Add 2x to the length and width. |wall. |

|Area = (1 + 2x) (w + 2x) |Side A: is ¼ of the perimeter (p). |

|[pic] |Side B: is ½ of the perimeter (p). |

| |Area = (¼p) (½p) |

PRACTICE PROBLEMS:

1) Find the maximum area of a rectangular pen whose perimeter is 100m.

2) Find the maximum area of a rectangular pen whose perimeter is 48 ft and borders a barn.

3) Find the maximum area of a rectangular yard that also borders a river and has a perimeter of 60ft.

4) Find the maximum area of a rectangular yard that has a perimeter of 32 ft.

5) The width of a photograph is 3 cm less than twice the length.

a. Write an equation for the area of the photograph.

b. If the area is 54 cm2, then find the dimensions of the photograph.

6) A square window is replaced by a rectangular one that is 3 ft wider and 2 ft higher than the square window.

a. Write the equation for the area of the new window.

b. If the area is 30 ft2, then what are the dimensions of the original square window.

7) A pool 5 yd by 6 yd is surrounded by a concrete deck of uniform width.

a. Write the equation for the area that the deck and pool cover.

b. If the area is 72 yd2, then how wide is the deck?

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width

length

¼ p

¼ p

¼ p

¼ p

½ p

¼ p

¼ p

x

x

x

x

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