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by sanju09 » Mon Mar 16, 2009 3:09 am
Semicircles (non-intersecting) are drawn taking the legs of a right-angled triangle as diameters. If hypotenuse of triangle measures 4, what is the sum of areas of the semicircles?

[spoiler]OA: 2 pi

'pi' the well known constant, in a circle, pi = its circumference/its diameter[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



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by praky_rules » Mon Mar 16, 2009 10:12 am
If the sides of the triangle are D1 and D2, the sum of the areas of the semi circles = pi/8*(D1^2+D2^2)=pi/8*4^2=2*pi
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by hamxa » Mon Mar 30, 2009 1:45 am
by legs of the triangle I also take hypotenuse and hence my answer comes out to be 4*pi.

Why did you not take hypo. as triangle leg ?
Please comment.

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by sanju09 » Mon Mar 30, 2009 2:46 am
hamxa wrote:by legs of the triangle I also take hypotenuse and hence my answer comes out to be 4*pi.

Why did you not take hypo. as triangle leg ?
Please comment.

Regards,
Whenever it comes to an isosceles triangle, its equal sides are referred to as its legs. It's a geometrical terminology :)
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by hamxa » Tue Mar 31, 2009 3:38 am
right angle triangle can be isosceles or scalene and also, in this question hypo. is 4 meaning: other 2 sides are not equal.
So even in this case we take 2 sides as the legs ?
Please clarify.
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by sanju09 » Tue Mar 31, 2009 3:53 am
hamxa wrote:right angle triangle can be isosceles or scalene and also, in this question hypo. is 4 meaning: other 2 sides are not equal.
So even in this case we take 2 sides as the legs ?
Please clarify.
:) Though the given is not an isosceles, but it never means that a right triangle with hypotenuse 4 cannot be isosceles. One more information about the use of term 'leg(s)' on geometry is that when it comes to right triangles, the sides including the right angle are also termed as legs. Please check this with other bonafide sources too.
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