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07 May 2020, 08:41
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C
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Difficulty:
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Question Stats:
77% (02:52) correct
23%
(02:24)
wrong
based on 53
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Points P, Q, R and S are on sides AB, BC, CD and DA of square ABCD, respectively, so that AP : PB = BQ : QC = CR : RD = DS : SA = 1 : n. What is the ratio of the area of PQRS to the area of ABCD ?
A. \(1 : (1 + n)\)
B. \(1 : n\)
C. \((1 + n^2) : (1 + n)^2\)
D. \((1 + n ) : (1 + n^2)\)
E. \(n : 1\)
Are You Up For the Challenge: 700 Level Questions
A. \(1 : (1 + n)\)
B. \(1 : n\)
C. \((1 + n^2) : (1 + n)^2\)
D. \((1 + n ) : (1 + n^2)\)
E. \(n : 1\)
Are You Up For the Challenge: 700 Level Questions
yashikaaggarwal
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07 May 2020, 09:01
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Answer is C.
The side of square ABCD is 1+n
The area of square ABCD is (1+n)^2 ----(1)
The side of square PQRS is (1+n^2)
Using Pythagoras Theorem,
In triangle APS
(AS)^2+(AP)^2=(PS)^2
(1)^2+(n)^2=(PS)^2
(PS)^2=1+n^2
(PS)=√(1+n^2)
Now the area of square PQRS is {√(1+n^2)}^2 = (1+n^2) ----(2)
The ratio of area of PQRS to area of ABCD
(1+n^2) : (1+n)^2
Answer is C
Posted from my mobile device
The side of square ABCD is 1+n
The area of square ABCD is (1+n)^2 ----(1)
The side of square PQRS is (1+n^2)
Using Pythagoras Theorem,
In triangle APS
(AS)^2+(AP)^2=(PS)^2
(1)^2+(n)^2=(PS)^2
(PS)^2=1+n^2
(PS)=√(1+n^2)
Now the area of square PQRS is {√(1+n^2)}^2 = (1+n^2) ----(2)
The ratio of area of PQRS to area of ABCD
(1+n^2) : (1+n)^2
Answer is C
Posted from my mobile device
07 May 2020, 09:46
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Bunuel
Let,
n = 3
and
Side of Square = 4
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