The length of the rectangle is 9 feet more than double the width. The perimeter of the rectangle is 78 feet. What is the length of the rectangle?

Answer 1

Since you're given value is the PERIMETER, 78ft., you want to add all the sides together and solve for your unknown variable.

The length of the rectangle is 9ft more than double the width. Therefore, L = 2w+9.

A rectangle has TWO sides that are known to be the length(s), meaning, to find the amount of ft of both sides you need to multiply by 2. Giving you:

L = 2(2w+9) .. simplified to --> 4w+18

A rectangle also has two sides known as the width. We weren't given a numerical value for the width so it will be labelled with the variable W.

To find the total amount of ft occupied by both sides known as the width we have to multiple by 2, giving: 2w.

Remember, they told you the total amount of feet of the perimeter, so when making your equation, set it equal to 78.

4w + 18 + 2w = 78

(simplify)

6w+18=78

(solve: subtract 18 from both sides)

6w=60

(solve: get the variable by itself by dividing)

w=10

....Now that you've found the Width (w=10) you can plug into the given equation for the length and solve for your final answer.

The length of the rectangle is 9ft more than double the width. L = 2w+9.

L = 2(10) + 9

= 20 + 9

L = 29

The length of your rectangle is 29 Feet. (DONT FORGET YOUR UNITS)

Want to check your work? Just plug in.

6w+18=78

6(10) + 18 = 78

60 + 18 = 78

78 = 78 √

Answer 2

Let's use the variable w to represent the width of the rectangle.

Then we can write the following expression to represent the length of the rectangle: 2w + 9

Since the perimeter of a rectangle is the sum of all four sides, we can write the following equation for this problem:

P = 2 • length + 2 • width

78 = 2 • (2w + 9) + 2 • w

Now we can use the distributive property and inverse operations to solve for w:

78 = 4•w + 18 + 2••w

78 = 6•w + 18

78 - 18 = 6 • w + 18 -18

60 = 6 • w

60/6 = 6 • w/6

10 = w

The width of the rectangle is 10 feet.

The length will be 2 • 10 + 9 = 29 feet