Question 1176144
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I will guess that the "heart" is a square with two semicircles of the same radius on the top edge of the square....<br>
Let x be the radius of each of the semicircles; then the side length of the square is 4x.<br>
The perimeter of the heart is then the length of 3 sides of the square plus the circumferences of the two semicircles -- {{{3(4x)+2(pi)(x) = x(12+2pi)}}}<br>
The maximum perimeter is 120cm:<br>
{{{x(12+2pi) = 120}}}
{{{x = 120/(12+2pi)}}}<br>
Use a calculator to find the value of x.<br>
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.<br>
The area of the heart is then {{{(4x)^2 + (pi)x^2}}}<br>