What is the surface area of the control panel if it is 4 times the surface area of the screen with a perimeter

univerkov | January 14, 2021 | education

What is the surface area of the control panel if it is 4 times the surface area of the screen with a perimeter of 16 dm and a width of 2 dm?

Let’s find the length of the screen surface.
Let’s denote it by x.
According to the condition of the problem, the perimeter of the screen is 16 dm, and the width of this screen is 2 dm.
The screen surface is rectangular, therefore, the screen perimeter can be calculated by multiplying the length and width of this screen by 2.
Therefore, we can make the following equation:
2 * (x + 2) = 16.
We solve the resulting equation:
x + 2 = 16/2;
x + 2 = 8;
x = 8 – 2;
x = 6 dm.
Knowing the length and width of the screen, we find its area S:
S = 6 * 2 = 12 dm².
According to the condition of the problem, the surface area of the control panel is 4 times greater than the surface area of the screen, therefore, the surface area of the control panel is:
12 * 4 = 48 dm².
Answer: the surface area of the control panel is 48 dm².

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