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.
