Perimeter = 2(Length) + 2(Width)
300 = 2L + 2W → 150 = L + W → 150 - L = W
Area = Length · Width
[tex] A_{max} [/tex] = L(150 - L) → [tex] A_{max} [/tex] = 150L - L²
There are 2 different methods for solving (depending on which math course you are taking).
Calculus: find the derivative, set it equal to zero, and solve for L.
[tex] A_{max} [/tex] = 150L - L² → 0 = 150 - 2L → 2L = 150 → L = 75
Algebra: find the vertex.
[tex] A_{max} [/tex] = - L² + 150L → L = -b/2a → L = -150/2(-1) → L = 75
Once you solve for L, plug it into the Perimeter equation to solve for W:
150 - L = W → 150 - 75 = W → W = 75
Answer: 75ft x 75ft
The dimensions that would yield the maximum area is 75 feet by 75 feet
A rectangle is a quadrilateral with four sides. The sum of angles in a rectangle add up to 360 degrees.
The area of a rectangle = length x width
The perimeter of a rectangle = 2 x ( length + width)
The first step to take in determining the answer, is to determine the sum of the dimensions of the rectangle
300 = 2 ( length + width)
300 / 2 = ( length + width)
( length + width) = 150
The sum of the length and the width is 150 feet
The second step is to determine the pairs of dimensions that would add up to 150.
Pair of dimensions:
150 x 1 = 150
5 x 145 = 725
10 x 140 = 1400
15 x 135 = 2025
20 x 130 = 2600
25 x 125 = 3125
30 x 120 = 3600
35 x 115 = 4025
40 x 110 = 4400
45 x 105 = 4725
50 x 100 = 5000
95 x 55 = 5225
75 x 75 = 5625
The dimensions that yield the highest area is 75 x 75 feet
To learn more about the perimeter of a rectangle, please check: brainly.com/question/18793958?referrer=searchResults
