Now You Try

<p>A pipe cleaner is 20 cm long. It is bent into a rectangle. Use a quadratic model to determine the dimensions that give the maximum area.</p>

<p>Harold wants to build five identical pig pens, side by side, on his farm using 30 m of fencing. Determine the dimensions of the enclosure that
would give his pigs the largest possible area. Calculate this area.</p>

<p>A rectangular picture frame measures 25 cm by 40 cm. A new frame is to be made by increasing each side length by the same amount. The total resulting enclosed area is to be <code class='latex inline'>1504 cm^2</code>. Find the dimensions of the new picture frame.</p>

<p>Nick has a beautiful rectangular garden, which measures <code class='latex inline'>3</code> m by <code class='latex inline'>3</code> m.
He wants to create a uniform border of river rocks around three sides
of his garden. If he wants the area of the border and the area of his
garden to be equal, how wide should the border be?</p>

<p>A pipe cleaner is 20 cm long. It is bent into a rectangle. Use a quadratic model to determine the dimensions that give the maximum area.</p>

<p>The length of a rectangular plot of land is <code class='latex inline'>7</code> m greater than its width. The diagonal is <code class='latex inline'>8</code> m greater than the width of the plot of land. What are the dimensions of the plot of land?</p>

<p>The length of a rectangle is <code class='latex inline'>2</code> cm more than the width. The area is <code class='latex inline'>24 cm^2</code>. What are the dimensions of the rectangle?</p>

<p>A television screen is <code class='latex inline'>40 cm</code> high and <code class='latex inline'>60 cm</code> wide. The picture is compressed to <code class='latex inline'>62.5\%</code> of its original area, leaving a uniform dark strip around the outside. What are the dimensions of the reduced picture?</p>

<p>A sprinkler waters a circular area of lawn of radius <code class='latex inline'>9</code> m. Another sprinkler waters an area that is <code class='latex inline'>100</code>% larger. What is the radius of lawn reached by the second sprinkler?</p>

<p>A rectangular garden measures 5 m by 7 m. Both dimensions are to be extended at both ends by the same amount so that the area of the garden is doubled. By how much should the dimensions increase. to the nearest tenth of a metre?</p>

<p> A rectangular field is to be enclosed and divided into two sections by a fence parallel to one of the sides using a total of 600 m of fencing. What is the maximum area that can be enclosed and what dimensions will give this area?</p>

<p>The playing surface in the game of curling is a rectangular sheet of ice with an area of about <code class='latex inline'>225 m^2</code>. The width is about 40 m less than the length. Find the approximate dimensions of the playing surface.</p>

<p>Write an algebraic expression to represent the area of the figure. Expand and simplify.</p><img src="/qimages/22334" />

<p>A field is bounded on one side by a river. The field is to be enclosed on three sides by a fence, to create a rectangular enclosure. The total length of fence to be used is 200 m. Use a quadratic model to determine the dimensions of the enclosure of maximum area.</p>

<p>The hypotenuse of a right triangle measures 29 cm. One leg is 1 cm shorter than the other. What are the lengths of the legs?</p>

<p> A rectangular solar-heat collecting panel's length is <code class='latex inline'>2.5 m</code> longer than it is wide. If its area is <code class='latex inline'>21 m^2</code>, what are its dimensions?</p>

<p>The grass in the backyard of a house is a square with side length <code class='latex inline'>10</code> m. A square patio is placed in the centre. If the side length, in metres, of the patio is <code class='latex inline'>x</code>, then the area of grass remaining is given by the relation <code class='latex inline'>A = -x^2 + 100</code>.</p><img src="/qimages/1814" />
<ul>
<li>How does the equation change if the grass in the backyard of a house is a square with side length 12 m?</li>
</ul>

<p>A room has dimensions of 5 m by 8 m. A rug covers <code class='latex inline'>\frac{3}{4}</code> of the floor and leaves a uniform strip of the floor exposed. How wide is the strip?</p>