SOLUTION: Heart modeled with a square and two semi-circles. You use red for the square and lighter red for the semi circles. the problem is you only have enough red for a perimeter of 120cm

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Question 1176144: Heart modeled with a square and two semi-circles. You use red for the square and lighter red for the semi circles. the problem is you only have enough red for a perimeter of 120cm per figure. If you maximize the squares what will be the area of the heart.
I think this is a quadratic but I am not sure any insight would be appreciated
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


I will guess that the "heart" is a square with two semicircles of the same radius on the top edge of the square....

Let x be the radius of each of the semicircles; then the side length of the square is 4x.

The perimeter of the heart is then the length of 3 sides of the square plus the circumferences of the two semicircles -- 3%284x%29%2B2%28pi%29%28x%29+=+x%2812%2B2pi%29

The maximum perimeter is 120cm:

x%2812%2B2pi%29+=+120
x+=+120%2F%2812%2B2pi%29

Use a calculator to find the value of x.

The area of the heart is the area of the square, plus the area of the two semicircles; the two semicircles together make a full circle.

The area of the heart is then %284x%29%5E2+%2B+%28pi%29x%5E2