Question

Triangle ABC and DEF are similar. What is the length of DF?*

Answer 1

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
​

Answer 2

Answer:

2.68

Step-by-step explanation:

2 is to 1.34 as 4 is to x

x=(4*1.34)/2