Question

Filipo is building a rectangular sandbox . The length of the sandbox is 1 foot longer than twice the width of the sandbox .the perimeter of the sandbox is 29 feet
Which equation could be used to determine w ,the width, in feet of the sand box?

A.) w + w + 2 = 29

B.) w + 2w + 1 = 29

C.) 2w + 2(w + 2) = 29

D.) 2w + 2(2w+ 1) = 29

Part B what is the length in feet of the sandbox

Answer 1

Answer:

Part A : D.) $2w + 2(2w+ 1) = 29$

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 = $2w+1$

Now we know that the perimeter is equal to the sum of twice of length and width.

framing in equation form, we get;

Perimeter = $2(2w+1)+2w$

we have given the perimeter, so on substituting the value, we get;

$29=2(2w+1)+2w$

Hence The equation used to find the width is  $29=2(2w+1)+2w$.

Now we solve for 'w'.

Applying distributive property, we get;

$4w+2+2w=29\\\\6w+2=29$

Subtracting both side by '2' we get

$6w+2-2=29-2\\\\6w=27$

Dividing both side by 6 we get;

$\frac{6w}{6}=\frac{27}{6}\\\\w=4.5\ ft$

Width of the sandbox = 4.5 ft

Length of the sandbox = $2w+1=2\times4.5 +1 = 9+1=10\ ft$

Hence Length of the sandbox is 10 feet.