Latest Elitmus Aptitude Question SOLUTION: A square ABCD shares 25% of its area with a rectangle AEFG, such that AE>AB and A, B, E are collinear. Also, rectangle AEFG shares 50% of its area with the square ABCD. Find AE/AG

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(#M40033155) ELITMUS Numerical Ability question Elitmus 23rd feb14 Keep an EYE

A square ABCD shares 25% of its area with a rectangle AEFG, such that AE>AB and A, B, E are collinear. Also, rectangle AEFG shares 50% of its area with the square ABCD. Find AE/AG.

Asked In Elitmus Vivek Jain (10 years ago)

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RAKESH  (10 years ago)

draw diagram,

let side of square =4x
length of rectangle = 2*4x = 8x [as,rectangle AEFG shares 50% of its area with the square ABCD]
breadth of rectangle= 4x/4 = x [as,square ABCD shares 25% of its area with rectangle AEFG]

so, AE=8x, AG=x => AE/AG = 8x/x = 8

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Sajal Garg  (10 years ago)

Let’s assume side of square is x
and side of rectangle is y
We know that A, B & E are Collinear , so our square & rectangle position with we like this
A-------------B------------E
| | |
G--------------------------F
| |
| |
| |
D-------------C
Let’s assume side of square is x=AB=BC=DC=AD
and other side of rectangle is y=AG=EF

According to condition, if A, B & E are in same line and rectangle share 50 % of its area with square than means
Rectangle ABOG=BEFO and from it we can make that AB=BE=x as we assumed.

Square area = x^2
Rectangle area = (2*x)*y…(because AE=2*x)
Cond 1) 25 % area of square shared with rectangle,
Cond2) 50% area of rectangle shared with square,
So by these condition we can conclude that 25% of square area equals with 50% of rectangle’s area,
Putting these we get, (x^2)/4={(2*x)*y}/2
=>x=4*y………………(i)

Need to FIND : AE/AG => (2*x)/y
Put eq (i) into this, (2*4*y)/y=8
Answer = 8 units

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kumod kumar  (9 years ago)

ans is 8:1.

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