Let:

The perimeter of a rectangle is , where  is the length and  is the width of the rectangle. The perimeter is known so we can set up an equation in terms of and solve it:

So we can get:

inches

inches

The perimeter of a rectangle is , where  is the length and  is the width of the rectangle. In order to find the perimeter we can substitute the  and  in the perimeter formula:

The length of the rectangle is known, so we can find the width in terms of :

The perimeter of a rectangle is , where  is the length and  is the width of the rectangle.

In order to find the perimeter we can substitute the  and  in the perimeter formula:

Substitute to get and :

The perimeter of a rectangle is  , where is the length and  is the width of the rectangle. So we have:

inches

Now we should divide the perimeter by 12 in order to convert to feet:

 feet

So the perimeter is 7 feet and 6 inches, which is between 7 and 8 feet.

The perimeter of a rectangle is twice the sum of its length and its width; a rectangle with dimensions 55 inches and 15 inches has perimeter 

 inches.

All of the polygons in the choices are regular - that is, all have congruent sides - and all have sidelength two feet, or 24 inches, so we divide 140 by 24 to determine how many sides such a polygon would need to have a perimeter equal to the rectangle. However, 

,

so there cannot be a regular polygon with these characteristics. All of the choices fail, so the correct response is that none are correct.

The area of Mark's lawn is . The amount of grass seed he needs is  pounds.

He has two options.

Option 1: he can buy three fifty-pound bags for 

Option 2: he can buy two fifty-pound bags and four ten-pound bags for 

The first option is the more economical. 

The area of a rectangle is given by multiplying the width times the height. As a formula:

Where:

is the width and is the height. So we can get:

The area of a parallelogram is given by:

Where is the base length and is the corresponding altitude. In this problem we have:

or

So the area of the parallelogram would be:

The area of a square is given by:

weher is the side length of a square. In this problem we have , so we can write:

Then:

or:

Solution 1:

We can divide the rectangle width and height by the square side length and multiply the results:

rectangle width square length =

rectangle heightsquare length =

Solution 2:

As the results of the division of rectangle width and height by the square length are integers and do not have a residual, we can say that the squares can be perfectly fitted in the rectangle. Now in order to find the number of squares we can divide the rectangle area by the square area:

Rectangle area = square inches

Square area = square inches

So we can get:

The area of a rectangle is given by multiplying the width times the height. That means:

where:

width and  height.

We know that: . Substitube the  in the area formula:

Now we should solve the equation for :

The equation has two answers, one positive  and one negative . As the length is always positive, the correct answer is inches.