Question

Chuck has 140 feet of fencing in which he wants to fence in two connecting, adjacent square pens with fencing between the two pens. What will be the dimensions of the length of the entire enclosed region is to be twice the width?

Answer 1

Answer:

280 feet.

Step-by-step explanation:

Chuck has 140 feet of fencing in which he wants to fence in two connecting, adjacent square pens with fencing between the two pens.

If the width of each pen is a feet, then (3a + 4a) = 7a will be the length of the fence.

So, 7a = 140

⇒ a = 20 feet

So, the length of the connecting adjacent pens will be twice the width of each pen.

If the width of the pens is 20 feet, then the length of the connected pens will be (20 × 2) = 40 feet. (Answer)

Answer 2

The dimensions of the entire closed region is 40 by 20 feet

Represent the length with l, and the width with w.

From the image of the fence (see attachment), we have:

$P = 3w + 2l$ -- the perimeter of the fence

The length of the entire region is twice the width.

So, we have:

$l = 2w$

Substitute 2w for l in $P = 3w + 2l$

$P = 3w + 2 \times 2w$

$P = 3w + 4w$

$P = 7w$

The perimeter of the fencing is 140 feet.

So, we have:

$7w = 140$

Divide both sides by 7

$w = 20$

Recall that:

$l = 2w$

This gives

$l = 2 \times 20$

$l = 40$

Hence, the dimensions of the entire closed region is 40 by 20 feet

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