A rectangular garden plot is to be enclosed with 40 meters of fences and find the area of the...

Question:

A rectangular garden plot is to be enclosed with 40 meters of fences and find the area of the garden as a function of the demensions of the recangle.

The Area of a Rectangle:

A rectangle is a quadrilateral that has 4 sides and 4 right angles. The opposite sides in a rectangle are congruent. We compute the area of a rectangle by multiplying its length by its width.

Answer and Explanation:


We calculate the area of a rectangle using the formula:

  • {eq}A = l\times w {/eq}

And the perimeter of a rectangle is given by:

  • {eq}P = 2(l + w) {/eq}

Given that a rectangle has a perimeter of 40 meters, we can express this as:

  • {eq}40 = 2(l + w) {/eq}

Solving for the width, we have:

  • {eq}20 = l + w {/eq}
  • {eq}w = 20 - l {/eq}

Therefore, the area of this rectangle can be expressed as:

  • {eq}A = l\times (20 - l) = 20l - l^2 {/eq}
  • {eq}A = \boxed{20l - l^2} {/eq}

Learn more about this topic:

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Measuring the Area of a Rectangle: Formula & Examples

from Geometry: High School

Chapter 8 / Lesson 7
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