Question

A rectangular garden must have a perimeter of 160 feet and an area of at least 1300 square feet. Describe the possible lengths of the garden. Round your answers to the nearest foot.
PLEASE HELP

Answer 1

Answer:

The possible lengths of the garden are 57.32 feet and 22.68 feet

Step-by-step explanation:

We all know that the perimeter of a rectangle is the addition of the length and the base multiplied by 2(ie [L×W]2).

If the perimeter of the rectangular garden is 160 feet and its area is 1300 square feet,we can get the lenght and the width of that particular garden having the shape of a rectangle.

Let's assume the lenght of the rectangle as X

And it's width as Y,we will have something that looks like this if we apply the area and perimeter

X × Y = 1300____________ equation 1

(X + Y) × 2 = 160

~ 2X + 2Y = 160_________ equation 2

From equation 1,we make x the subject of the formula so as to find x

X = 1300/Y

Substitute "X = 1300/Y in equation 2

2(1300/Y) + 2Y = 160

Open up the bracket above

2600/Y + 2Y = 160

(2600 + 2Y²)/Y = 160

2600 + 2Y² = 160y

2Y² - 160Y + 2600 = 0

Factorize the above quadratic equation and we have

y = 57.32 or 22.68 feet's.

The width will be 22.68 feet since its the smaller figure of the 2 figures

AND the length will be 57.32 feet.

Now let's check to see if we are correct about the figures we got.

Remember that the area of the rectangle is length × width

57.32 × 22.68 = 1300 square feet.

And the perimeter which is 2L + 2W

114.64 + 45.36 = 160 feet

Answer 2

Answer: The lengths of the garden are 57.32 feet and 22.68 feet (approximately)

Step-by-step explanation: The area has been given as 1300 which means,

Area = L x W

1300 = L x W ———(1)

Also the perimeter has been given as 160, hence we also have

Perimeter = 2(L + W)

160 = 2(L + W)

80 = L + W ———(2)

From equation (2), make L the subject of the equation

L = 80 - W

Substitute for the value of L into equation (1)

1300 = L x W

1300 = (80 - W) x W

1300 = 80W - W^2

Rearranging the equation we now have;

W^2 - 80W + 1300 = 0

Since we cannot factorize we shall apply the quadratic equation formula to solve for W. Please refer to the attachment for details of this.

Having calculated the value of W to be either 57.32 or 22.68, we can now find the value of L as follows;

Substitute for the value of W into equation (1)

1300 = L x W

1300 = L x 57.32

Divide both sides of the equation by 57.32

22.68 = L.

(Note that if we take the other value of W which is 22.68, the value of L shall be 57.32)

Since the area of the rectangular garden must be AT LEAST 1300 square feet we shall use the exact values for;

Length = 57.32 feet

Width = 22.68 feet