1 point
tringle ABC and tringe DEF are similar. Area of AABC is 9 cm?
and area of ADEF is 64 cm² . If DE = 5.1 cm, then
find the value of AB.
Answers
Answer:
(i) We know that the ratio of area of two similar triangles is equal to the ratio of squares of their corresponding sides.
∴
area(△DEF)
area(△ABC)
=(
EF
BC
)
2
⇒
25
16
=(
EF
2.3
)
2
⇒
5
4
=
EF
2.3
⇒ EF=
4
2.3×5
∴ EF=2.875cm
(ii) We know that the ratio of area of two similar triangles is equal to the ratio of squares of their corresponding sides.
∴
area(△DEF)
area(△ABC)
=(
DE
AB
)
2
⇒
64
9
=(
DE
AB
)
2
⇒
8
3
=
5.1
AB
∴ AB=1.91cm
(iii) We know that the ratio of area of two similar triangles is equal to the ratio of squares of their corresponding sides.
∴
area(△DEF)
area(△ABC)
=(
DF
AC
)
2
∴
area(△DEF)
area(△ABC)
=(
8
19
)
2
∴
area(△DEF)
area(△ABC)
=(
64
361
)
(iv) We know that the ratio of area of two similar triangles is equal to the ratio of squares of their corresponding sides
∴
area(△DEF)
area(△ABC)
=(
DE
AB
)
2
⇒
64
36
=(
DE
AB
)
2
⇒
8
6
=
6.2
AB
∴ AB=4.65cm
(v) We know that the ratio of area of two similar triangles is equal to the ratio of squares of their corresponding sides.
∴
area(△DEF)
area(△ABC)
=(
DE
AB
)
2
∴
area(△DEF)
area(△ABC)
=(
1.4
1.2
)
2
∴
area(△DEF)
area(△ABC)
=
49
36