The length of a rectangle is 3yd longer than its width. If the perimeter of the rectangle is 62yd, find its length and width.

Question

finding width and length given equation

Answer 1

In Geometry, it is a given that the perimeter of a rectangle is the sum of the length of all sides. Therefore we can say that the Perimeter (P) is equal to 2xLength (L) + 2xWidth (W)

So, P = 2L + 2W

Now what?

Well, we know that the Length of the rectangle is 3 yards longer than its Width. Therefore, L = W + 3.

Now we can subsitute this into the perimeter equation in order to have only W's in there.

P = 2(W+3) + 2W

Let's simplify:

P = 2W + 2x3 + 2W

P = 2W + 6 + 2W

P = 4W + 6

We can add the two W's since they are the same variable.

Now, knowing that P = 62 yards, we cal plug this into the equation to solve for W, since it will be the only remaining variable.

62 = 4W + 6

Now we just have to solve for W using simple arithmetic.

62 - 6 = 4W

56 = 4W

56/4 = W

14 = W

Now we know that the Width is 14 yards, we can use this information to solve for the Length, because we know that the Length is 3 yards longer than the Width. This ties back to earlier in the problem.

L = W + 3

Now substituting in the actual value of W and solving for L:

L = 14 + 3

L = 17

Therefore, the Width is 14 yards and the Length is 17 yards!

Please contact me if you have any further questions. :)

Answer 2

To find the perimeter of the rectangle, you had to add twice the length of the rectangle to twice the width of the rectangle since the shape of a rectangle is made up of two legs (each representing the rectangle's length) and two legs (each representing the rectangle's width.

The perimeter can be mathematically seen as p = 2l+2w, where p is the amount corresponding to the perimeter of the rectangle, l is the amount representing the length of the rectangle, and w is the quantity reflecting the width of the rectangle. This equation can be modified using the equation l = w+3, since it is given that the length is 3 yards longer than the width.

Therefore, the p = 2l+2w equation can be modified to solve for w using the given conditions and the equation defining l.

p = 2l+2w

p = 2(w+3)+2w [Substituting l = w+3]

p = 2w+6+2w

p = 4w+6

p-6 = 4w+6-6

p-6 = 4w

(p-6)/4 = 4w/4

w = (p-6)/4

w = (62-6)/4 [Substituting given conditions for perimeter]

w = 56/4

w = 14

Now the length of the rectangle can be determined using the equation l = w+3.

l = 14+3 = 17

Therefore, the length of the rectangle is 17 yards and the width of the rectangle is 14 yards.

Answer 3

Hi Dylan!

The formula for calculating the perimeter of a rectangle is as follows:

1. P = 2 * ( L + W )
2. Where P= perimeter
3. L = Length of the rectangle
4. W = Width of the rectangle

The information we are given:

1. P = 62 yd
2. L = W+ 3 (Length = Width + 3 yd)

To solve this, we want to simplify the number of variables we are given so that we can solve for one at a time. Based on the information we've been given, we can substitute the variable for Length. Now, we can take a look at the equation for Perimeter again:

1. Before: P = 2 * ( L + W )
2. Now: P = 2 * (( W+3) + W) or P = 2 * ( 2W + 3 )

We can distribute that 2, and simplify our equation.

1. P = 4W + 6

Now we can solve for W!

1. 62 = 4W + 6

Subtract 6 from both sides:

1. 56 = 4W

Divide by 4:

1. W = 14 yd

We now have the solution for W! We can use this information to solve for L, based on our substitution before.

1. L = W + 3 or L = 14 +3
2. Our solution is L = 17 and W = 14