Answer:
Step-by-step explanation:
The first part of finding the length and width of this rectangle is defining each of the lengths as variables. We usually do this by writing, "let" for each statement. Let's try!
Let x = the width
2x + 3 = the length
Now, let's define the perimeter in terms of x. So, we understand that the perimeter consists of the width times 2 and the length times 2. It's simply how rectangles work, right? Let's do this, then! Let's find the perimeter in terms of x!
2(x) + 2(2x + 3)=
=2x + 4x + 6
=6x + 6
Considering the width of the rectangle is x and the length is 2x + 3, the perimeter of the rectangle is 6x + 6. But hey, we already know what the actual perimeter of the rectangle is! Let's make a system of equations! (We're getting a little advanced here but it's alright, ask me questions if you need to!)
Let P = total perimeter of the rectangle
P = 6x + 6
P = 128 feet
We can solve this system of equations by using the equal values method. If you need more help, you can search the equal values method on the internet. If you need more explanation, please ask!
Now we know that both 6x + 6 and 128 are both equal to P. This means that 6x + 6 and 128 are equal, too! We can now make an equation to find x, the width!
6x + 6 = 128
- 6 - 6
6x = 122
x = 122/6 = 20 ¹/₃ feet
Since we have already defined x as 20 1/3 feet. Now we can find the length, 2x + 3. We can plug x into the equation.
2 ( 20 ¹/₃ ) + 3 = length
40 ²/₃ + 3 = length
length = 43 ²/₃.
Now we can check our work!
6x + 6 = 128
6(20 ¹/₃) + 6 = 128
6(20 ¹/₃) = 122
If we multiply 6 and 20 ¹/₃, we find the product as 122. This means that x is true in the situation and that it is correct.
If you need help, please tell me in the comments! I'm happy to help! <3
