Bunuel wrote:

What is the total area of the figure, if the area of the shaded region is 100 and MK = 10?
(1) x = y = 45
(2) QL = 10
Attachment:
The attachment image008.jpg is no longer available
Question stem:- What is the area of the quadrilateral KMNL?
St1:-
x = y = 45Refer the enclosed diagram, \(\triangle{NQL}\), \(\triangle{KPO}\), and \(\triangle{KMP}\) are isosceles right angled triangles(45-45-90) form. sides are in the ratio \(x:x:\sqrt{2}x\)
So base=height=10 and hypotenuse=\(10\sqrt{2}\)
Hence area of \(\triangle{NQL}\)=Area of \(\triangle{KPO}\)=Area of \(\triangle{KMP}\) (Base and height are known, area can be determined)
Total area of figure=Area of shaded region(100)+3*Area of triangle NQL
Sufficient.
St-2:- QL = 10
Area of the figure will be different at different measures of x.
Insufficient.
Ans. (D)Edit: Fixed typo. Ans. (A)
Attachments

Area.JPG [ 17.05 KiB | Viewed 640 times ]
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Regards,
PKN
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