given triangle Abc similar to triangle def find the area of triangle Abc divided by area of triangle def.if A and d = 90 degree,ab=3cm,DF=12 and EF =13cm.
Answers
Answer:
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Step-by-step explanation:
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
Given: Triangle ABC similar to triangle DEF. A and D = 90 degree, AB = 3 cm, DF = 12 and EF = 13 cm.
To find: The area of triangle ABC divided by area of triangle DEF.
Solution:
In the triangles ABC and DEF, ∠A and ∠D are 90°. So, they are right-angled triangles. In triangle DEF, the perpendicular is 12 cm and the hypotenuse is 13 cm. Hence, the base can be found using the Pythagoras theorem.
Since the two triangles are similar, their sides are in proportion. The proportion can be represented as follows.
In the two triangles, AC and DF form the perpendicular and the length of the perpendicular is the height of the triangle. The area of a triangle is given by the formula,
The area of triangle ABC divided by the area of triangle DEF can be calculated as,
Therefore, the area of triangle ABC divided by area of triangle DEF is 0.36.