Question

sam wants to fence his rectangular garden plot along its length on the front side. The perimeter of the plot is 24 meters, and its length is 3 times its width

Answer 1

From the given information, there are two equations in terms of x and y:

2x + 2y = 24 (perimeter of the rectangular plot)

x = 3y (relationship between length and width)

The second equation is expressed in terms of x, so directly substitute the value of x into the first equation and find y:

2(3y) + 2y = 24

y = 3

Substitute y in the second equation to find x:

x = 3(3)

x = 9

The fencing cost is $25 multiplied by the length of the side Sam wants to fence: 25 × 9 = 225. Therefore, Sam needs to spend $225 to fence that side of his plot.

Explanation:

Answer 2

Length: 12 meters

Explanation:

Step 1:

Let us start with the formula of the perimeter of a rectangle,
`P=2l+2w`, where l represents the length of the rectangle, and w represents the width of the rectangle.

We can set width as variable x. We are also given that the length is three times the width, hence it can be represented as 3x.

Step 2:

We can now write our equation and solve for x :

`24=2x+2*2x\\24=2x+4x\\24=6x\\x=\fbox{4}`

We set x as width, so the width is 4 meters. However, in this problem we are looking for the length. The length is three times the width, so it would be
`\fbox{12}` meters.

I hope this helps! Let me know if you have any questions :)