Mathematics: The area of a rectangle is 81cm^2 what are the dimensions if the perimeter is minimum. What is the value of these minimum perimeter?

The area of a rectangle is 81cm^2 what are the dimensions

Ответ:

liamgreene90

17.06.2021

Mathematics

The perimeter is 36 cm

Step-by-step explanation:

Given;

area of the rectangle, A = 81 cm²

let the Length, = L

let the breadth = b

Perimeter, P = 2L + 2b

Area, A = Lb = 81

$L = \frac{81}{b} \\\\P = 2(\frac{81}{b} ) \ + \ 2b\\\\P = \frac{162}{b} \ + \ 2b\\\\P = 162(b^{-1}) \ + \ 2b\\\\minimize \ the \ perimeter \ to \ obtain \ the \ critical \ points;\\\\P' = -162 (b^{-2}) \ + \ 2\\\\P' = \frac{-162}{b^2} \ + \ 2\\\\P' = \frac{-162 \ + \ 2b^2}{b^2} \\\\at \ critical \ points; P' = 0\\\\\frac{-162 \ + \ 2b^2}{b^2} = 0\\\\-162 \ + \ 2b^2 = 0\\\\2b^2 = 162\\\\b^2 = 81\\\\b = +/- \ \sqrt{81} \\\\b = +/- \ \ 9\\\\$

$since \ the \ breadth \ will \ be \ positive \ ; b = 9 \ cm$

L = 81/9

L = 9 cm

The perimeter = 2 (L + b)

= 2 (9 + 9)

= 2(18)

= 36 cm

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Ответ:

jameslinimk

01.01.2021

Mathematics

The 3rd semi-circle equals 31.

Step-by-step explanation:

Since the Pythagorean Theorem states that "The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c)," we can find the answer of the 3rd semi-circle by finding the sum of each of the 2 smaller semi-circles and adding them together.

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The area of a rectangle is 81cm^2 what are the dimensions if the perimeter is minimum. What is the value of these minimum perimeter?

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