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Zorluk: OrtaRatios, Rates, and Proportions

A web designer is creating a layout with three sections: a header, a main content area, and a sidebar. The ratio of the area of the header to the area of the main content area is 1:31:3. The ratio of the area of the main content area to the area of the sidebar is 4:34:3. If the total area of the layout is 2,0002,000 square pixels, what is the area, in square pixels, of the sidebar?

  1. A
    320
  2. 720Cevap
  3. C
    960
  4. D
    1,000
  5. E
    1,500

Cevap

720
The correct answer is 720 square pixels. To find this, combine the ratios H:M=1:3H:M = 1:3 (which scales to 4:124:12) and M:S=4:3M:S = 4:3 (which scales to 12:912:9) using their common term MM. This yields a joint ratio of H:M:S=4:12:9H:M:S = 4:12:9. Let the areas be 4x4x, 12x12x, and 9x9x. The sum is 25x=2,00025x = 2,000, which gives x=80x = 80. The sidebar area is 9x=9(80)=7209x = 9(80) = 720 square pixels.

Adım Adım Çözüm

1
Express the ratios with a common term.
The ratio of the header to the main content is H:M=1:3H:M = 1:3, which is equivalent to 4:124:12. The ratio of the main content to the sidebar is M:S=4:3M:S = 4:3, which is equivalent to 12:912:9. Combining these gives a joint ratio of H:M:S=4:12:9H:M:S = 4:12:9.
Finding a common term for the main content area (MM) allows us to express all three sections in a single ratio.
2
Set up an equation for the total area in terms of a multiplier xx.
4x+12x+9x=2,000⇒25x=2,0004x + 12x + 9x = 2,000 \Rightarrow 25x = 2,000
The sum of the individual areas must equal the total area of 2,0002,000 square pixels.
3
Solve for xx.
x=80x = 80
This determines the value of one part of the ratio.
4
Calculate the area of the sidebar.
9×80=7209 \times 80 = 720
The sidebar's area is represented by 9x9x, so we multiply 99 by 8080.

Anahtar Kavram

Combining multiple ratios through a common term to solve multi-part ratio problems.
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Konular

Ratios, Rates, and Proportions

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