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Byju's Answer
Standard X
Mathematics
Relation between Areas and Sides of Similar Triangles
ABC DEF If A...
Question
ABC
~
DEF
If AB= 2.4 cm and DE= 1.6 cm, find the ratio of the areas of
△
ABC and
△
DEF.
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Solution
Since
△
ABC
~
△
DEF
,
A
(
△
ABC
)
A
(
△
DEF
)
=
AB
2
DE
2
=
BC
2
EF
2
=
AC
2
DF
2
⇒
A
(
△
ABC
)
A
(
△
DEF
)
=
AB
2
DE
2
On
substituting
AB
=
2
.
4
cm
and
DE
=
1
.
6
cm
,
we
get
:
A
(
△
ABC
)
A
(
△
DEF
)
=
(
2
.
4
)
2
(
1
.
6
)
2
⇒
A
(
△
ABC
)
A
(
△
DEF
)
=
2
.
4
1
.
6
2
=
3
2
2
⇒
A
(
△
ABC
)
A
(
△
DEF
)
=
9
4
Thus
,
A
△
ABC
:
A
(
△
DEF
)
=
9
:
4
.
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Similar questions
Q.
ABC
~
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If AB= 2.4 cm and DE= 1.6 cm, find the ratio of the areas of
△
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△
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Q.
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△
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△
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Q.
Triangles ABC and DEF are similar.
(i) If area (∆ABC) = 16 cm
2
, area (∆DEF) = 25 cm
2
and BC = 2.3 cm, find EF.
(ii) If area (∆ABC) = 9 cm
2
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2
and DE = 5.1 cm , find AB.
(iii) If AC = 19 cm and DF = 8 cm, find the ratio of the area of two triangles.
(iv) If area (∆ABC) = 36 cm
2
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2
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(v) If AB = 1.2 cm and DE = 1.4 cm, find the ratio of the areas of ∆ABC and ∆DEF.