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Question

An ecology center wants to set up an experimental garden using three hundred meters of fencing to enclose a rectangular area of five thousand square meters.

(a) Let $x$ meters represent the width of the garden. Why must the length be $150-x$ meters?

(b) Write an expression $\mathscr{A}(x)$ that represents the area of the garden.

(c) What are the restrictions on $x$ ?

(d) Use the given values for area and length of fencing to find the dimensions of the garden.

Solution

VerifiedStep 1

1 of 7$2x+2y=300$

$2y=300-2x$

$y=\dfrac{300-2x}{2}=\dfrac{2(150-x}{2}=150-x$

a) Let's note:

$x$=the width of the rectangle

$y$=the length of the rectangle.

We determine $y$ in terms of $x$ using the perimeter:

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