emmak wrote:

A painting at an art gallery is framed such that the area of the square frame is 1/4 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 10, what is the area of the painting inside the frame?

a) 10

b) 20

c) 30

d) 40

e) 50

Figure attached

Suppose side of the painting(which is a square) is "a" and side of the outer square(paiting+frame) is "b"

Area of paiting = a^2 and we know that the area of the frame is (1/4) of that of the paiting so

Area of frame = (1/4) * a^2

Area of Frame + Paiting = a^2 + (1/4)*a^2 = (5/4)*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 = 10

so, b = 5 * sqrt2

b^2 = 50

we know that b^2 = (5/4)*a^2

so, a^2 = (4/5)*b^2 = (4/5)*50 = 40

And area of paiting = a^2 = 40

So, answer will be D.

Hope it helps!

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Ankit

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