College

The length of a rectangular garden is 7 feet longer than its width. The garden's perimeter is 186 feet. Find the width of the garden.

Answer :

We have a rectangular garden. The length of the garden is 7 feet longer than its width.

Lets say the width of the garden is 'x' feet. So, the length of the garden must be [tex](x+7)[/tex] feet.

Length [tex]=(x+7)[/tex] feet

Width [tex]=x[/tex] feet

We have been given that the perimeter of the garden is 186 feet.

Now as we know that the perimeter of the rectangle is:

[tex]2(length+width)[/tex]

Plugging the values of length and width in the equation, we get:

Perimeter [tex]= 2((x+7)+x)=2(2x+7)=4x+14[/tex]

We know that perimeter of the garden is equal to 186 feet,

So,

[tex]186=4x+14[/tex]

Solving for 'x' we get:

[tex]4x+14=186[/tex]

[tex]4x=186-14=172[/tex]

[tex]x=\frac{172}{4} =43[/tex]

We had assumed that the width of the garden is 'x' feet and now that we have the value of 'x'. We can say that:

The width of the rectangular garden is 43 feet.


The width of the garden is found by using the perimeter formula for a rectangle and the given information that the length is 7 feet longer than the width. Solving the resulting equation gives a width of 43 feet.

To find the width of the garden, we use the fact that the perimeter (P) of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. We are told that the length is 7 feet longer than the width, so we can express the length as w + 7. Substituting the given perimeter of 186 feet, we set up the equation as follows: 186 = 2(w + 7) + 2w. Simplifying further, we get 186 = 4w + 14. Subtracting 14 from both sides gives us 172 = 4w and dividing both sides by 4, we find w = 43. Therefore, the width of the garden is 43 feet.