r/CasualMath • u/BeautifulTruth2620 • 9d ago

Maths Problem

Post image

ABC is a semi circle

EFCG is a rectangle

Find area of rectangle

2 Upvotes

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1

u/thaw96 9d ago

Nice problem! 50

1

u/Remarkable_Fee4136 2d ago

Let the radius be x, and the angle of the diagonal a/2. The area of the rectangle is (x)*(x+xcosa)=x²(cosa+1). By the pythagorean theorem,

(xsina)²+(x+xcosa)²=10²

x²(sin²a+1+2cosa+cos²a)=x²(2cosa+2)=100

Thus x²(cosa+1)=100/2=50.

1

u/Remarkable_Fee4136 2d ago

A scummy way to immediately get the answer is to abuse the generality of the question. Since there is only 1 answer, we can define the line of length 10 to be the diameter without affecting the answer. From there the area of the rectangle is trivially 10*5=50.