Acarpenter is building a rectangular room with a fixed perimeter of 300 ft. what dimensions would yield the maximum area?

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: link

Perimeter = 2(Length) + 2(Width)

300 = 2L + 2W → 150 = L + W → 150 - L = W

Area = Length · Width

= L(150 - L) → = 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.

= 150L - L² → 0 = 150 - 2L → 2L = 150 → L = 75

Algebra: find the vertex.

= - 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

75ft x 75ft

step-by-step explanation:

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