Answer:
Area: 240x² - 72x - 240
Perimeter: 64x + 28
Dimensions: <em>l</em> = 60, <em>w</em> = 50
Step-by-step explanation:
<u>For Area:</u>
<u>Multiply length by width.</u>
(12x + 24) • (20x - 10)
<u>Let's foil this out (first, outer, inner, last)</u>
240x² - 120x + 48x - 240
<u>Simplify.</u>
240x² - 72x - 240
<u>For Perimeter</u>
Remember that a rectangle has <em>two</em> sets of matching parallel sides.
<u>Let's write out our equation.</u>
2(12x + 24) + 2(20x - 10)
<u>Distribute and break it down.</u>
24x + 48 + 40x - 20
<u>Simplify.</u>
64x + 28
<u>Perimeter For Given Value</u>
Now we'll solve for if the perimeter was 220 feet.
<u>Let's use the perimeter equation from above to find x.</u>
64x + 28 = 220
64x = 192
x = 3
<u>Now that we know x is 3, we'll substitute it into the equations in your question.</u>
12(3) + 24 20(3) - 10
36 + 24 60 - 10
60 50
The length is 60ft and the width is 50 ft.