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Difficulty:
45%
(medium)
Question Stats:
67% (02:19) correct
33%
(02:42)
wrong
based on 235
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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
A. 10
B. 20
C. 30
D. 40
E. 50
Updated on: 29 Oct 2022, 09:52
Originally posted by BrushMyQuant on 12 Mar 2013, 23:26.
Last edited by BrushMyQuant on 29 Oct 2022, 09:52, edited 1 time in total.
Last edited by BrushMyQuant on 29 Oct 2022, 09:52, edited 1 time in total.
Given that 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. And we need to find If the diagonal line connecting corners of the frame has a length of 10, what is the area of the painting inside the frame?
Figure attached
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 (1/4) of that of the painting so
Area of frame = (1/4) * a^2
Area of Frame + Painting = 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 painting = a^2 = 40
So, Answer will be D.
Hope it helps!
_________________
Figure attached
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 (1/4) of that of the painting so
Area of frame = (1/4) * a^2
Area of Frame + Painting = 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 painting = a^2 = 40
So, Answer will be D.
Hope it helps!
Attachments
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_________________
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GMAT Club Topic Wise Problems
All Quant Topics Theory || Last Two Digits of Exponents Ending with 1, 2, 3, 4, 5, 6, 7, 8, 9 || Units' Digit Problems || Even and Odd || Divisibility Rules || Positive and Negative || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot
GMAT Club Topic Wise Problems
It has been established that both the painting and the frame are square.
So let the side of the frame be 'A' and the side of the painting be 'a'
It is stated that \(A^2-a^2 = \frac{1}{4}*a^2\)
It has also stated that the diagonal of the frame is 10, so \(\sqrt{2}*A = 10\)
So \(A=\frac{10}{\sqrt{2}}\) which implies \(A^2=50\)
\(50-a^2 = \frac{1}{4}*a^2\)
\(50 = \frac{5}{4}*a^2\)
So, \(a^2 = 40\)
Answer is D
So let the side of the frame be 'A' and the side of the painting be 'a'
It is stated that \(A^2-a^2 = \frac{1}{4}*a^2\)
It has also stated that the diagonal of the frame is 10, so \(\sqrt{2}*A = 10\)
So \(A=\frac{10}{\sqrt{2}}\) which implies \(A^2=50\)
\(50-a^2 = \frac{1}{4}*a^2\)
\(50 = \frac{5}{4}*a^2\)
So, \(a^2 = 40\)
Answer is D
emmak
Start the solution with what is given to you in the question. You may not need to use any variables in that case.
Diagonal = 10
Then, side of the frame = \(5\sqrt{2}\)
Area of the entire painting + frame = \((5\sqrt{2})^2 = 50\)
Since area of frame is 1/4th of the area of painting,
Area of frame = 10 and Area of painting = 40
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Posts: 46
VeritasPrepKarishma
Oh , that's such a neat way !
Posts: 11
emmak
Let d=diagonal length
Area of a square = \(\frac{d^2}{2}\)
So the entire area of the Frame + Painting would be.
\(A= \frac{10^2}{2}\)
\(A= \frac{100}{2}\)
\(A= 50\)
We know that the area of the frame is 1/4 that of the painting. So it is clear that the frame is 10 and the painting is 40.
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Apologies I understand it a bit better now, but i was confused by the question wording.
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