Question

Karma is building a rectangular table with an area of 18,000 cm?. He wants to put wood trim around the four edges. What is the shortest length of trim he could use (nearest to hundredth)?​

Answer 1

The shortest length is given by the function for the perimeter of the

rectangular table.

• The shortest length of trim he could use is 536.66 cm

Method used for finding the shortest length of trim

The given parameter;

Area of the rectangular table Karma is building, A = 18,000 cm²

Required:

The shortest length of trim he could use which he wants to put around the four edges.

Solution:

Let l represent the length of the table, and let w represent the width, therefore;

Perimeter of the table, P = 2·l + 2·w

Area, A = l × w

Which gives;

18,000 = l × w

$l = \dfrac{18,000}{w}$

Which gives;

$P = 2 \cdot \dfrac{18,000}{w} + 2 \cdot w$

At the minimum point, we have;

$\dfrac{d}{dw} P = \dfrac{d}{dw} \left(2 \cdot \dfrac{18,000}{w} + 2 \cdot w\right)= \mathbf{\dfrac{2 \cdot w^2 - 36,000}{w^2} }= 0$

Which gives;

2·w² - 36,000 = w² × 0 = 0

2·w² = 36,000

$w^2 = \dfrac{36,000}{2} = 18,000$

The width of the rectangular table, w = √(18,000)

$Length \ of \ the \ table\ l = \dfrac{18,000}{\sqrt{18,000} } = \sqrt{18,000}$

Therefore;

The perimeter of the table, P ≈ 2 × √(18,000) + 2 × √(18,000) ≈ 536.656

The length of trim required = The perimeter of the rectangular table, P

Therefore;

• The shortest length of the trim he could use, given to the nearest hundredth is 536.66 cm

Learn more about area and perimeter of a figure here:

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