Find Area Formula of Rectangle

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SUMMARY

The discussion focuses on deriving the area formula for a rectangle given a fixed perimeter of 30 feet. The perimeter equation is established as P = 2L + 2W, leading to the expression for length L in terms of width x: L = (30 - 2x)/2. The area A is then formulated as A = x(15 - x), confirming that the length and width of a rectangle sum to half the perimeter.

PREREQUISITES
  • Understanding of basic algebraic manipulation
  • Knowledge of perimeter and area formulas for rectangles
  • Familiarity with variables and equations
  • Ability to simplify algebraic expressions
NEXT STEPS
  • Study the derivation of area formulas for other geometric shapes
  • Explore optimization techniques for maximizing area given constraints
  • Learn about the relationship between perimeter and area in different polygons
  • Investigate real-world applications of area calculations in design and architecture
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Students in mathematics, educators teaching geometry, and anyone interested in understanding the relationship between perimeter and area in rectangular shapes.

mathdad
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Let x denote the width of a rectangle with perimeter 30 feet. Find the area of this rectangle.

Let me see.

P = 2L + 2W

30 = 2L + 2x

(30 - 2x) = 2L

(30 - 2x)/2 = L

A = LW

A = [(30 - 2x)/2]x

Correct?

I guess we can simplify a little more.

A = x(15 - x)

Correct?
 
Mathematics news on Phys.org
yes ... the length & width of a rectangle sum to half the perimeter

$P = 2(L+W) \implies L+W = \dfrac{P}{2}$
 
Good to be right.
 

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