Answer:
Part A : D.) [tex]2w + 2(2w+ 1) = 29[/tex]
Part B : Length of the sandbox is 10 feet.
Step-by-step explanation:
Given,
Perimeter = 29 ft
We need to find the equation for the perimeter and also the length of the sandbox.
Solution,
Let the width of the sandbox be 'w'.
Now as per question said;
The length of the sandbox is 1 foot longer than twice the width of the sandbox.
So we can say that;
Length = [tex]2w+1[/tex]
Now we know that the perimeter is equal to the sum of twice of length and width.
framing in equation form, we get;
Perimeter = [tex]2(2w+1)+2w[/tex]
we have given the perimeter, so on substituting the value, we get;
[tex]29=2(2w+1)+2w[/tex]
Hence The equation used to find the width is [tex]29=2(2w+1)+2w[/tex].
Now we solve for 'w'.
Applying distributive property, we get;
[tex]4w+2+2w=29\\\\6w+2=29[/tex]
Subtracting both side by '2' we get
[tex]6w+2-2=29-2\\\\6w=27[/tex]
Dividing both side by 6 we get;
[tex]\frac{6w}{6}=\frac{27}{6}\\\\w=4.5\ ft[/tex]
Width of the sandbox = 4.5 ft
Length of the sandbox = [tex]2w+1=2\times4.5 +1 = 9+1=10\ ft[/tex]
Hence Length of the sandbox is 10 feet.
Answer:
Part A : D
Part B : Length of the sandbox is 10 feet amd the width is 4.5 feet.
