1. [1pt] A rectangle has an area of 1000m2. Let x be the length of the rectangle

Question

1. [1pt] A rectangle has an area of 1000m2. Let x be the length of the rectangle and let y be the width of the rectangle. Find the function describing the perimeter of this rectangle. Write the perimeter as a function of one variable, the variable x.

2. [2pts] A candy box is to be made out of a piece of cardboard that measures 8 by 12 inches. Squares of equal size will be cut out of each corner, and then the ends and sides will be folded up to form a rectangular box. Let x be the side measure of the square piece that is cut out of each corner. Find the function describing the volume of this box.

3. [2pts] A box with a square base and an open top must have a volume of 32,000cm3. Let x be the side measure of the square base. Find the function describing the surface area of the box. Write the surface area as a function of one variable, the variable x.

Explanation / Answer

1) area of rectangle = 1000 m^2

length = x

width = y

xy = 1000

y = 1000/ x

perimeter of rectangle = 2 ( l + w )

or 2 ( x+ y )

so we can write perimeter as

2 ( x + 1000/ x )

Perimeter as a function of x = ( 2 x^2 + 2000) / x

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