Question

(35 points) The length of a rectangle is 3 meters more than twice its width. If the perimeter of the rectangle is 50 meters, what is the length and the width of the rectangle? Write your answer as an exact number.

Length: ____meters Width:_____meters

Answer 1

Let's call the width of the rectangle "W" meters.

According to the problem, the length of the rectangle is 3 meters more than twice its width, which can be expressed as:

Length = 2W + 3 meters

The perimeter of a rectangle is given by the formula:

Perimeter = 2(Length + Width)

In this case, the perimeter is 50 meters. So, we can write:

50 = 2(2W + 3 + W)

Now, let's solve for W:

50 = 2(3W + 3)

Divide both sides by 2:

25 = 3W + 3

Subtract 3 from both sides:

22 = 3W

Now, divide by 3:

W = 22 / 3

W = 7.33 meters (rounded to two decimal places)

So, the width of the rectangle is approximately 7.33 meters.

Now, we can find the length using the earlier formula:

Length = 2W + 3

Length = 2(7.33) + 3

Length = 14.66 + 3

Length = 17.66 meters

So, the length of the rectangle is approximately 17.66 meters.

Length: 17.66 meters

Width: 7.33 meters

Answer 2

Length: 17.66 meters

Width: 7.33 meters

Explanation:

Let the width of the rectangle be w, so the length of the rectangle is 3+2w.

We have:

Length = 3 + 2w

Width = w

Since Perimeter of rectangle = 2(length + width)

We can set up the following equation for the perimeter by substituting value, we get

50 = 2(w + 3+2w)

Simplify like terms in right side:

50 = 2(3w+3)

Distribute 2 on right side:

50 = 6w + 6

Subtract 6 on both sides:

50 - 6= 6w + 6 - 6

44 = 6w

Divide both sides by 6, we get

`\sf (44)/(6) =( 6w)/(6)`

w = 7.33

Therefore, the width of the rectangle is 7.33 meters and the length of the rectangle is 3+2 × 7.33 = 17.66 meters.

So the answer is:

Length: 17.66 meters

Width: 7.33 meters