the ratio of the corresponding sides of the two similar triangles is 1:3, then the ratio of their areas is
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We know that if two triangles are similar then
(Area of triangle 1)/(Area of triangle 2) =(sideof 1st triangle )^2/(corresponding side of triangle 1 in2 triangle)^2
Area1/area2=(1/3)^2=1/9
(Area of triangle 1)/(Area of triangle 2) =(sideof 1st triangle )^2/(corresponding side of triangle 1 in2 triangle)^2
Area1/area2=(1/3)^2=1/9
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Solution ;-
Ratio of the corresponding sides of the two similar triangles = 1 : 3
We know that if two triangles are similar, then the ratio of the area of the both the triangles is proportional to square of the ratio of their respective corresponding sides.
To prove this theorem, let us consider two similar triangles Δ ABC Δ XYZ.
Ratio of corresponding two sides of the two similar triangles = 1 : 3
= 1/3
Then, the ratio of the area of Δ ABC/area of Δ XYZ = (1/3)²
= 1/9 = 1 : 9
The ratio of their areas is 1 : 9
Answer
Ratio of the corresponding sides of the two similar triangles = 1 : 3
We know that if two triangles are similar, then the ratio of the area of the both the triangles is proportional to square of the ratio of their respective corresponding sides.
To prove this theorem, let us consider two similar triangles Δ ABC Δ XYZ.
Ratio of corresponding two sides of the two similar triangles = 1 : 3
= 1/3
Then, the ratio of the area of Δ ABC/area of Δ XYZ = (1/3)²
= 1/9 = 1 : 9
The ratio of their areas is 1 : 9
Answer
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