The ratio of the areas of two similar triangles ABC and PQR is 25 : 144 .What is the ratio of their medians AM and PN
Answers
Answer:
If two triangles are equals than the ratio of their square is equal to the ratio of their corresponding sides.
∴
arc(△PQR)
arc(△ABC)
=
QR
2
BC
2
⇒
49
25
=
(9.8)
2
BC
2
⇒
7
5 =
9.8
BC
⇒BC=
7
9.8×5
=7.0cm
2
Given : The ratio of the areas of two similar triangles ABC and PQR is 25:144.
To Find : Ratio of their medians AM and PN
Solution:
For Similar triangle Ratio of corresponding sides is Equal and corresponding angles are equal.
ΔABC ~ ΔPQR
Ratio of Area of similar triangle = ( Ratio of corresponding sides)²
=> 25/144 = ( Ratio of corresponding side)²
=> (5/12)² = ( Ratio of corresponding side)²
=> Ratio of corresponding side = 5/12
AB/PQ = AC/PR = BC/QR = 5/12
In similar triangles
Ratio of corresponding Medians =Ratio of corresponding side
=> Ratio of corresponding Medians = 5/12
AM/PN = 5/12
ratio of their medians AM and PN = 5 :12
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