contestada

The length of a rectangular garden is 8 feet longer than it’s width. The garden is surrounded by a sidewalk that is 4 feet wide and has a area of 320 square feet. Find the dimensions of the garden.

Respuesta :

Hussam7
Answer:

The length = 20
The width = 12 

Explanation:

Let the Length of the garden be L and the Width W 
Therefore the area of the garden = L*W 
But we know that L = W + 8 
Therefore the area of the garden can be expressed as W*(W + 8) 
When the brackets are expanded this equals W^2 + 8W

The area of the recctangle which includes the path and garden will have a length of L + 8 (ie the length of the garden + 4 feet at the top and 4 feet at the bottom) 
The width will be W + 8 (width of garden + 4 feet at the left and 4 feet at the right) 
Therefore the area will be (W + 8)*(L +8) 
Once again we know that L = W + 8 
Therefore the area of the path/garden = (W +8)(W +8 +8) 
=(W +8)(W +16) 
=W^2 +24W + 128 

We know that the path alone has an area of 320 square feet. Therefore if we subtract the area of the garden (W^2 + 8W) from the area of the path/garden the area left is the area of the path only 

Therefore W^2 + 24W + 128 - (W^2 + 8W) = 320 
W^2 + 24W + 128 - W^2 - 8W = 320 
Simplify 
16W + 128 = 320 
Subtract 128 from both sides of the equation 
16W = 192 
divide both sides of the equation by 16 
W = 12 
As L = W + 8 
L = 12 + 8 = 20 

The length of the garden is 20 feet and the width of the garden is 12 feet.

Given

The length of a rectangular garden is 8 feet longer than its width.

The garden is surrounded by a sidewalk that is 4 feet wide and has an area of 320 square feet.

How to calculate the dimension of the garden?

Let the Length of the garden be L and the Width W.

The length of the garden L = W + 8

The width of the garden is W(W + 8).

Then,

The area of the path/garden is;

[tex]\rm Area = (W +8)\times (W +8 +8) \\\\ Area = (W +8)\times (W +16) \\\\Area = W(W+16)+8(W+16)\\\\Area=W^2+16W+8W+128\\\\Area=W^2+24W+128[/tex]

Therefore,

The dimension of the garden is;

[tex]\rm W^2 + 24W + 128 - (W^2 + 8W) = 320 \\\\W^2 + 24W + 128 - W^2 - 8W = 320 \\\\16W=320-128\\\\16W=192\\\\W=\dfrac{192}{16}\\\\W=12[/tex]

The length of the garden L = W + 8 = 12 + 8 = 20 feet

Hence, the length of the garden is 20 feet and the width of the garden is 12 feet.

To know more about the area click the link given below.

https://brainly.com/question/4728191

Otras preguntas