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geometry

by sud21 » Fri Jan 13, 2012 5:34 am
In the figure shown above, ABC is a right triangle, and three rectangles are square. What is the area of the largest square?
1). The sum of area of two small squares is given.
2). The area of the triangle is given.


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by neelgandham » Sat Jan 14, 2012 12:15 pm
In the figure shown above, ABC is a right triangle, and if the three rectangles are squares. What is the area of the largest square?

if a,b,c are the length of sides of the right angles triangle where the side with length c units is the hypotenuse, then a^2 + b^2 = c^2 (Pythagorean theorem).
1). The sum of area of two small squares is given.
Area of square of side a = a^2
Area of square of side b = b^2
Area of square of side c = c^2 = a^2 + b^2(Pythagorean theorem). Since the value of a^2 + b^2 is given statement 1 is sufficient to answer the question
2). The area of the triangle is given.
0.5*a*b = given. But for a constant product of two numbers we get loads of combinations. for e.g.
if 0.5*a*b = 1/2 then ab = 1. so (a,b) can be (2,1/2),(3,1/3),(4,1/4) etc..
Insufficient to answer the question

IMO A
p.s: I am not really sure of the source of the question but I,somehow ,don't feel that the question is properly framed including the options.
Anil Gandham
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