Question

The perimeter of a rectangle is 28 m. The length is 2

m more than three times the width. Find the length
and the width of the rectangle.

Answer 1

Let's denote the width of the rectangle as w and the length as l.

According to the problem, we have two conditions:

1. The length is 2 m more than three times the width. This gives us the equation l = 3w + 2.

2. The perimeter of a rectangle is twice the sum of its length and its width, which gives us the equation P = 2(l + w). Substituting P = 28, we get 28 = 2(l + w).

Now, let's substitute the first equation into the second to solve for w:

28 = 2((3w + 2) + w) = 2(4w + 2) = 8w + 4

Subtract 4 from both sides:

24 = 8w

Divide both sides by 8 to solve for w:

w = 24 / 8 = 3 meters

Substitute w = 3 into the first equation to find l:

l = 3 * 3 + 2 = 9 + 2 = 11 meters

So, the width of the rectangle is 3 meters, and the length is 11 meters.

Answer 2

Explanation:

Let's assume the width of the rectangle is represented by "w" meters.

According to the given information, the length of the rectangle is 2 meters more than three times the width, which can be expressed as "3w + 2" meters.

The perimeter of a rectangle is given by the formula: 2(length + width).

We can now set up the equation using the given perimeter of 28 meters:

2(3w + 2 + w) = 28

Simplifying the equation:

2(4w + 2) = 28

8w + 4 = 28

8w = 28 - 4

8w = 24

w = 24/8

w = 3

Therefore, the width of the rectangle is 3 meters.

To find the length, we substitute the value of the width back into the expression for the length:

Length = 3w + 2

Length = 3(3) + 2

Length = 9 + 2

Length = 11

Hence, the length of the rectangle is 11 meters.

In summary, the width of the rectangle is 3 meters, and the length is 11 meters.