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Byju's Answer
Standard X
Mathematics
Relation between Areas and Sides of Similar Triangles
If Δ ABC ∼Δ...
Question
If
Δ
A
B
C
∼
Δ
P
Q
R
and
P
Q
A
B
=
5
2
then area
(
Δ
A
B
C
)
:
area
(
Δ
P
Q
R
)
=
?
A
25
:
4
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B
4
:
25
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C
5
:
2
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D
25
:
2
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Solution
The correct option is
A
4
:
25
Given that,
Δ
A
B
C
∼
Δ
P
Q
R
Also,
P
Q
A
B
=
5
2
To find out: Ratio of the areas of the two triangles.
We know that, if triangles are similar, then the ratio of their areas is equal to the square of the ratio of their sides.
∴
a
r
e
a
(
A
B
C
)
a
r
e
a
(
P
Q
R
)
=
(
A
B
P
Q
)
2
=
(
2
5
)
2
[
∵
P
Q
A
B
=
5
2
⇒
A
B
P
Q
=
2
5
]
.
=
4
25
Hence, the required ratio is
4
:
25
.
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0
Similar questions
Q.
Δ
A
B
C
and
Δ
P
Q
R
are two similar triangles shown in the figure. AM and PN are the medians on
Δ
A
B
C
and
Δ
P
Q
R
, respectively. The ratio of areas of
Δ
A
B
C
and
Δ
P
Q
R
is 9:25. If AM = PO = 5 cm. Find the value of 3(ON).
Q.
If
Δ
A
B
C
∼
Δ
P
Q
R
and
Δ
P
Q
R
∼
Δ
X
Y
Z
,
then
Δ
A
B
C
∼
Δ
X
Y
Z
Q.
In
Δ
A
B
C
∼
Δ
P
Q
R
,
M
is the midpoint of
B
C
and
N
is the midpoint of
Q
R
. The area of
Δ
A
B
C
=
100
sq. cm and the area of
Δ
P
Q
R
=
144
sq. cm. If
A
M
=
4
cm, then
P
N
is:
Q.
Δ
A
B
C
and
Δ
P
Q
R
are two similar triangles shown in the figure. AM and PN are the medians on
Δ
A
B
C
and
Δ
P
Q
R
, respectively. The ratio of areas of
Δ
A
B
C
and
Δ
P
Q
R
is 9:25. If AM = PO = 5 cm. Find the value of 3(ON).
Q.
Δ
P
Q
R
is formed by joining the midpoints of
Δ
A
B
C
.
Find the area of the
Δ
P
Q
R
if the area of the
Δ
A
B
C
is
52
c
m
2
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