If ∆ABC ~ ∆PQR and AB : PQ = 2 : 3, then fill in the blanks
Practice Set 1.4 | Q 2 | Page 25
If ∆ABC ~ ∆PQR and AB : PQ = 2 : 3, then fill in the blanks.\[\frac{A\left( ∆ ABC \right)}{A\left( ∆ PQR \right)} = \frac{{AB}^2}{……} = \frac{2^2}{3^2} = \frac{……}{…….}\]
Given:
∆ABC ~ ∆PQR
AB : PQ = 2 : 3
According to theorem of areas of similar triangles "When two triangles are similar, the ratio of areas of those triangles is equal to the ratio of the squares of their corresponding sides".
\[\therefore \frac{A\left( ∆ ABC \right)}{A\left( ∆ PQR \right)} = \frac{{AB}^2}{{PQ}^2} = \frac{2^2}{3^2} = \frac{4}{9}\]
Answer:-
Given: ∆ABC ~ ∆PQR and AB : PQ = 2 : 3
To find: The ratio of the areas of the two triangles.
Solution: According to the theorem of areas of similar triangles, “when two triangles are similar, the ratio of areas of those triangles is equal to the ratio of the squares of their corresponding sides.”
Therefore, we have:
A(∆ABC) / A(∆PQR) = (AB / PQ)²- Substituting the given ratio of AB : PQ = 2 : 3, we get:
A(∆ABC) / A(∆PQR) = (2 / 3)² - Simplifying, we get:
A(∆ABC) / A(∆PQR) = 4 / 9 - Therefore, the ratio of the areas of the two triangles is 4 : 9.
Chapter 1. Similarity- Practice Set 1.4 – Page 25
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