The length of a rectangle is nine more than the width. If the perimter of the rectangle is 62​ feet,what are the length and​ width?

width --- x

length ---x+9

2x + 2(x+9) = 62
2x + 2x + 18 = 62
4x = 44
x = 11

the width is 11 and the length is 20

check:
2(11) + 2(20) = 62 , as needed

Why did the rectangle bring a calculator to the party? Because it loves to calculate its own dimensions! 😄

Let's solve this math problem step by step. We know that the length (L) of the rectangle is nine more than the width (W). So we can express that as L = W + 9.

The perimeter (P) of a rectangle is given by the formula P = 2L + 2W. We are told that the perimeter is 62 feet, so we can write this equation as 62 = 2L + 2W.

Now we can substitute the value of L from the first equation into the second equation.

62 = 2(W + 9) + 2W

Simplifying the equation:

62 = 2W + 18 + 2W

Combining like terms:

62 = 4W + 18

Subtracting 18 from both sides:

44 = 4W

Dividing both sides by 4:

W = 11

Now we can substitute the value of W back into the first equation to find L:

L = W + 9
L = 11 + 9
L = 20

So the width of the rectangle is 11 feet, and the length is 20 feet.

Let's let "w" represent the width of the rectangle.

According to the problem, the length of the rectangle is "nine more" than the width. So the length would be "w + 9".

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

Given that the perimeter of the rectangle is 62 feet, we can set up the equation:

62 = 2(w + 9 + w)

Simplifying the equation:

62 = 2(2w + 9)

Divide both sides of the equation by 2 to solve for "w":

31 = 2w + 9

Subtract 9 from both sides of the equation:

31 - 9 = 2w

22 = 2w

Divide both sides of the equation by 2:

11 = w

So the width of the rectangle is 11 feet.

Now, substitute the value of "w" back into the expression for the length:

Length = Width + 9
Length = 11 + 9
Length = 20 feet

Therefore, the length of the rectangle is 20 feet and the width is 11 feet.

To find the length and width of the rectangle, we will first set up an equation based on the given information.

Let's assume the width of the rectangle is "w" feet.

According to the given information, the length of the rectangle is nine more than the width, which means the length would be "w + 9" feet.

Now, let's calculate the perimeter of the rectangle using the formula: perimeter = 2(length + width).

Given that the perimeter is 62 feet, we can substitute the values into the equation:

62 = 2(w + 9 + w)

Simplifying the equation:
62 = 2(2w + 9)
62 = 4w + 18

Next, we subtract 18 from both sides of the equation:
62 - 18 = 4w
44 = 4w

Now divide both sides of the equation by 4:
44/4 = 4w/4
11 = w

Therefore, the width of the rectangle is 11 feet.

To find the length, we substitute the value of the width back into the equation w + 9:
11 + 9 = 20

Therefore, the length of the rectangle is 20 feet.

Hence, the width of the rectangle is 11 feet, and the length is 20 feet.

width = 11

lenght = 18