Olympiad workbookIOQMStraight Lines
Let A B C D be a rectangle in which A B+B C+ C D=20 and A E=9 where E is the mid-point of the side B C . Find the area of the rectangle.
Correct answer
19
Step-by-step solution
aligned & 2 x+y=20 & y=20-2 x ...(i) & In A B E aligned x^2+ ( y 2 )^2=9^2 ...(ii) Using (i) in (ii) aligned & x^2+ ( 20-2 x 2 )^2=81 & x^2+(10-x)^2=81 & 2 x^2-20 x+19=0 & x= 20 400-4 2 19 2 2 & x= 10 62 2 aligned From (i) aligned y & =20-2 ( 10 62 2 ) y & =10 62 aligned aligned Area of rectangle =x y & = 1 2 (10 62 )(10 62 ) & = 100-62 2 & =19 aligned