Dimensions of a rectangular garden
We are going to follow the step-by-step:
Step 1 - naming each unkown dimension
Step 2 - finding two equations
Step 3 - finding the width and length
Step 4 - sum of the dimensions
Step 1 - naming each unkown dimension
We want to find the length and width of the rectangular garden. We are going to name both with a letter:
L: length
W: width
Step 2 - finding two equations
Based on the given information, we find a mathematical expression.
First equation
The length of a rectangular garden is 3 feet more than four times the width. This is
L is 3 feet more than 4 times W.
4 times W = 4W
If L is 3 feet more than 4W, then
L = 4W + 3
Second equation
The perimeter of the garden is 66 feet.
We know that the perimeter of a rectangle is the sum of all its sides:
length + width + length + width = 2length + 2 width = 2L + 2W
Then,
2L + 2W = 66
Step 3 - finding the width and length
Now, we want to solve the equations we found:
L = 4W + 3
2L + 2W = 66
we are going to do it using Substitution.
Finding the width
We substitute
L = 4W + 3
on the second equation:
2L + 2W = 66
↓ replacing L by 4W + 3
2(4W + 3) + 2W = 66
Now we have an equation with just one varible, so we can find W:
2(4W + 3) + 2W = 66
↓ distributive property 2(4W + 3) = 8W + 6
8W + 6 + 2W = 66
↓ since 8W + 2W = 10W
10W + 6 = 66
↓ taking 6 to the right side
10W = 66 - 6
↓ since 66 - 6 = 60
10W = 60
↓ taking 14 to the right side
W = 60/10
W = 6
Finding the length
Now we replace in any of the equations to find L (it will always be the same result). We use the frist equation we find:
L = 4W + 3
↓ replacing W by 6
L = 4 · 6 + 3
↓ since 4 · 6 + 3 = 27
L = 27
Step 4 - sum of the dimensions
We have that
W = 6 and L = 27, then their sum is
W + L = 6 + 27 = 33
Answer- D. 33