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
[tex]l = \dfrac{18,000}{w}[/tex]
Which gives;
[tex]P = 2 \cdot \dfrac{18,000}{w} + 2 \cdot w[/tex]
At the minimum point, we have;
[tex]\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[/tex]
Which gives;
2·w² - 36,000 = w² × 0 = 0
2·w² = 36,000
[tex]w^2 = \dfrac{36,000}{2} = 18,000[/tex]
The width of the rectangular table, w = √(18,000)
[tex]Length \ of \ the \ table\ l = \dfrac{18,000}{\sqrt{18,000} } = \sqrt{18,000}[/tex]
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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