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The area of a rectangle is 1 square inches. Express the perimeter P(w) as a function of the width w.

2 Answers

3 votes

Answer:


P(w)=2w+(2)/(w)

Explanation:

We are given the area of a rectangle is 1 inch square.

You can find the area of a rectangle if you know the dimensions. Let's pretend the dimensions are w and l.

So we given w*l=1.

Now the perimeter of a rectangle with dimensions l and w is 2w+2l.

We want to express P=2w+2l in terms of w only.

We are given that w*l=1 so l=1/w (just divided both sides of w*l=1 by w).

So let's plug it in for l (the 1/w thing).


P=2w+2((1)/(w))

So
P(w)=2w+(2)/(w).

User MoneyBall
by
8.0k points
2 votes

Answer:

P (w) =
(2)/(w) +2w

Explanation:

We are given that the area of a rectangle is 1 square inches and we are to express the perimeter
P(w) as a function of the width
w.

We know that:

Area of a rectangle =
l * w

Substituting the given value of area in the above formula:


1=l * w


l=(1)/(w)

Perimeter of a rectangle =
2(l +w)

Substituting the values in the formula to get:

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

User Joeltine
by
8.2k points

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