1.fill in the blanks:-
1.5.If △DEF=△ACB,then the part of △ACB that corresponds to ∠F is _________.
2.64% + 20% +___________=100%.
3.The ratios 8:2 and 16:4 are equivalent therefore8,2,16 and 4 are in _________.
4.For a given △ART and △PEN,if ∠T=∠N,RT=EN and PN=AT then △ART=△PEN under _________ criterion.
Answers
Answer:
Given △ABC∼△DEF
Hence the ratio of their areas is the ratio of squares of their sides
∴ar(△DEF)ar(△ABC)=DE2AB2
⇒4520=DE225
∴DE=7.5 cm
Step-by-step explanation:
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If two triangles are similar then the sides of one triangle are proportional to (i.e., in the same ratio of ) the sides of the other triangle.
As △ACB∼△APQ
So
AP
AC
=
PQ
CB
=
AQ
AB
2.8
AC
=
5
10
=
AQ
6.5
2.8
AC
=2=
AQ
6.5
Hence AC=2×2.8=5.6cm
Also AQ=
2
6.5
=3.25cm
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
area(△APQ)
area(△ACB)
=
AP
2
AC
2
area(△APQ)
area(△ACB)
=(
2.8
5.6
)
2
area(△APQ)
area(△ACB)
=2
2
=4
Hence
area(△APQ)
area(△ACB)
=4
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