For a rectangle,  and , where  is the length and  is the width.

Let  be equal to the width. We know that the length is equal to "two more than twice with width."

The equation to solve for the perimeter becomes .

Now that we know the width, we can solve for the length.

Now we can find the area using .

First, we need to convert the length and width of the rectangle into similiar units.

Now, calculate the area.

We are given the rectangle's diagonal  and width  and are asked to find its area. The diagonal forms two right triangles within the rectangle; therefore, we can use the Pythagorean theorem to find the length of the rectangle's missing side. Then we can use the formula  to find the are of the rectangle.

In our case, we can rename the variables to match our triangle.

Now we can calculate the area.

This problem requires you to find both the perimeter (fence) and the area (grass seed) of a rectangle where and .

Fence Problem (Perimeter):

Grass Seed Problem (Area):

So the total cost for both projects is .

Since a rectangle has  pairs of equal-length sides, multiplying each side by  and adding the products together gives the perimeter of the rectangle. Use this fact to set up an equation with the given information about the rectangle's sides and perimeter. Solving for  in this equation will provide necessary information for finding the rectangle's area:

Multiplying the measure of the long side of the rectangle by the measure of the short side of the rectangle gives the rectangle's area. The length of the long side is given by substituting the solution for  into the given expression  that defines its length. The short side is , giving the following equation to calculate the area:

 units squared

The area of the larger rectangle is calculated as  units squared. Since the ratio of the larger to the smaller rectangle is , dividing the larger rectangle's area by  gives the area of the smaller rectangle:

 units squared

First, find the area of the rectangular yard:

 square feet

Next, find the area of the round cement fountain:

square feet

Then find the difference between the two:

square feet

Now, to get the number of grass seed bags needed, divide the area by to get approximately bags.  Because one can't purchase a partial bag, the correct answer is the next largest whole number, or bags of grass seed.

The width of the rectangle is w, therefore the length is 3w.  The perimeter, P, can then be described as P = w + w + 3w +3w

                                                                                          40 = 8w

                                                                                          w = 5

                                                                                          width = 5, length = 3w = 15

                                                                                          A = 5*15 = 75 square inches

First, we need to find the area of the room. Because the room is rectangular, we can multiply 20 feet by 30 feet, which is 600 square feet. Next, we need to know how much space one carpet piece covers. Because the carpet pieces are also rectangular, we can multiply 4 feet by 5 feet to get 20 feet. To determine how many pieces of carpet Angela will need, we must divide the total square footage of the room (600 feet) by the square footage covered by one carpet piece (20 feet). 600 divided by 20 is 30, so Angela will need 30 carpet pieces to carpet the entire room.

the length of the rectangle is half the width, and the width is 8, so the length must be half of 8, which is 4.

The area of the rectangle can be determined from multiplying length by width, so,

4 x 8 = 32 inches squared