Question

Perimeter of two equilateral triangles ABC and PQR are 144m and 96m, find ar (∆ABC) : ar (∆PQR).

Answer 1

Given:

PERIMETER of equilateral  ∆ABC = 144 m
PERIMETER of equilateral ∆PQR = 96 m

In equilateral ∆ all three sides are equal.

In ∆ABC, AB=BC=AC
In ∆PQR, PQ= QR = PR

Equilateral ∆’s are similar
∆ABC ~ ∆PQR

PERIMETER of  ∆ABC/PERIMETER of ∆PQR = AB/PQ

[If two Triangles are similar ,then the corresponding sides are proportional and they are proportional to the corresponding perimeters.
144/96 = AB /PQ
3/2 = AB/PQ
AB/PQ = 3/2

∆ABC/∆PQR= AB²/PQ²

[The ratio of areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides]

ar(∆ABC)/ar (∆PQR) = 3²/2² = 9/4
∆ABC/∆PQR = 9/4
∆ABC : ∆PQR = 9:4

Hence, the ar(∆ABC) : ar (∆PQR) = 9:4

HOPE THIS WILL HELP YOU...

Answer 2

HEY.......
HERE IS U R ANSWER
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LENGHT OF SIDE OF ΔABC = 144/3 = 48
AREA OF ABC = √3/4* 48 * 48
= 576√3

LENGHT OF SIDE OF PQR = 96/3 = 32
AREA = √3/4 * 32 *32
= 256√3

Ratio= 576√3 / 256√3
= 576 / 256

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HOPE IT WILL HELP YOU A LOT....
THANKU.....