Question

(b) Perimeters of two similar triangles are 40 cm and
60 em respectively. Find ratio among their areas.
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Answer 1

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We know the ratio of perimeters of two similar triangles is same as ratio of their corresponding sides.

and

The ratio of areas of two similar triangles is equal to square of their corresponding sides.

Let ABC and DEF are two similar triangles.

Perimeter of triangle ️ ABC = 40 CM

Perimeter of triangle ️ DEF = 60 CM

Perimeter of Triangle ️ ABC : Perimeter of Triangle ️ DEF = AB : DE

40 : 60 = AB : DE

2 : 3 = AB : DE

Now,

Area of ️ ABC : Area of ️ DEF = AB^2 : DE^2

= 2^2 : 3^2

= 4 : 9.

Answer 2

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• We know the ratio of perimeters of two similar triangles is same as ratio of their corresponding sides.

• The ratio of areas of two similar triangles is equal to square of their corresponding sides.

Let ABC and DEF are two similar triangles.

Perimeter of triangle ️ ABC = 40 CM

Perimeter of triangle ️ DEF = 60 CM

Perimeter of Triangle ️ ABC : Perimeter of Triangle ️ DEF = AB : DE

40 : 60 = AB : DE

2 : 3 = AB : DE

Now,

Area of ️ ABC : Area of ️ DEF = AB² : DE²

= 2² : 3²

= 4 : 9.

Thanks..