The ratio of corresponding sides of similar triangles is 3 : 5; then Find the ratio of their areas..
Practice Set 1.4 | Q 1 | Page 25
The ratio of corresponding sides of similar triangles is 3 : 5; then Find the ratio of their areas..
Let the ratio of corresponding sides of similar triangles be S1 and S2 and A1 and A2 be their corresponding areas.
∴ S1: S2 = 3: 5 ...(Given)
∴ `("S"_1)/("S"_2) = 3/5` ...(i)
The two triangles are similar. ...(Given)
by Theorem of areas of similar triangle,
`("A"_1)/("A"_2) = ("S"_1)^2/("S"_2)^2`
`("A"_1)/("A"_2) = (("S"_1)/("S"_2))^2`
`("A"_1)/("A"_2) = (3/5)^2` ...[From (i)]
`("A"_1)/("A"_2) = 9/25`
∴ Ratio of areas of similar triangles = 9: 25.
Answer:-
To find the ratio of the areas of two similar triangles, we can use the fact that the ratio of their corresponding sides is equal to the square root of the ratio of their areas. Let the ratio of corresponding sides of the two triangles be 3:5, which means that the longer side of the second triangle is 5/3 times the longer side of the first triangle.
Then, let the areas of the two triangles be A1 and A2, respectively. We have:
A1/A2 = (corresponding side of triangle 1 / corresponding side of triangle 2)^2 A1/A2 = (3/5)^2 A1/A2 = 9/25
Therefore, the ratio of the areas of the two similar triangles is 9:25.
Chapter 1. Similarity- Practice Set 1.4 – Page 25
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