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Standard VIII
Mathematics
Similarity
The ratio of ...
Question
The ratio of the area of a square to that of the square drawn on its diagonal is
A
1 : 1
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B
1 : 2
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C
1 : 3
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D
1 : 4
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Solution
The correct option is
B
1 : 2
Let the side of square is x
Then side of diagonal=
√
(
s
i
d
e
)
2
+
(
s
i
d
e
)
2
=
√
x
2
+
x
2
=
√
2
x
2
=
√
2
x
Then area of square(A)=
x
2
And
Then area of square on diagonal (D)=
(
√
2
x
)
2
=
2
x
2
Then
area of square(A) :
area of square on diagonal (D)=
x
2
:
2
x
2
=
1
:
2
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