A painting at an art gallery is framed such that the area of the square frame is 1/5 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 12, what is the area of the painting inside the frame?  Choose the correct choice:
A) 10
B) 20
C) 30
D) 40
E) 60
Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b   Area of painting = a^2 and we know that the area of the frame is (1/5) of that of the painting so   Area of frame = (1/5) * a^2   Area of Frame + Painting = a^2 + (1/5)*a^2 = (6/5)*a^2 which is equal to b^2   Line connecting the corners of the frame is the diagonal of the outer square which is equal to b*sqrt2   so, b * sqrt2 = 12   so, b = 6 * sqrt2   b^2 = 72   we know that b^2 = (6/5)*a^2   so, a^2 = (5/6)*b^2 = (5/6)*72= 
<gadget id="calculator">(5/6)*72</gadget>
<output>60</output>
60   And area of painting= a^2 = 60   So, answer will be 60.
<result>E</result>
A painting at an art gallery is framed such that the area of the square frame is 1/5 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 12, what is the area of the painting inside the frame?