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A window is in the form of a semicircle surmounted over a rectangle. Thew total perimeter of the window is 12m.

Note:This is a part of a maxima minima question that I was trying to solve. I could solve it but my answer was different from other students because of the difference in the question of perimeter that I and they wrote.

My equation for perimeter:2(x+y)+(pi)(x/2)

Other's eq. for perimeter:2y+x+(pi)(x/2).

I also considered the middle line separating the semicircle and the rectangle. Which one is correct. If it is not to be considered they should have given 'outer periemter of the window' in the question.

enter image description here

Rajath Radhakrishnan
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2 Answers2

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If $x$ represents the full width of the rectangle, as one might set it up:

There should be only one copy of $x$ added, the bottom of the window. The other piece of length $x$ running to bound off the semicircle is not part of the perimeter.

If $x$ represents only half the width of the rectangle, your version should have $\pi x$ for the part from the semicircle, rather than $\pi x /2$ as you have it.

coffeemath
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Generally, perimeter means the length of the shape's boundary, not including the inner line separating the rectangle and the circular part.

So here the perimeter is $2x+2y+\pi x$. I assume that the $x$ is taken as the radius of the circular shape, as shown in the figure.

L__
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