Areas of two similar triangles are 225 sq.cm. 81 sq.cm. If a side of the smaller triangle is 12 cm,
Practice Set 1.4 | Q 5 | Page 25
Areas of two similar triangles are 225 sq.cm. 81 sq.cm. If a side of the smaller triangle is 12 cm, then Find corresponding side of the bigger triangle.
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".
\[\therefore \frac{\text{ Area of bigger triangle }}{\text{ Area of smaller triangle }} = \frac{225}{81}\]
\[ \Rightarrow \frac{\left( \text{ Side of bigger triangle } \right)^2}{\left( \text{ Side of smaller triangle } \right)^2} = \frac{{15}^2}{9^2}\]
\[ \Rightarrow \frac{\text{ Side of bigger triangle }}{\text{ Side of smaller triangle }} = \frac{15}{9}\]
\[\Rightarrow \text{ Side of bigger triangle } = \frac{15}{9} \times \text{ Side of smaller triangle }\]
\[ \Rightarrow \text{ Side of bigger triangle } = \frac{15}{9} \times 12\]
\[ = 20\]
Hence, the corresponding side of the bigger triangle is 20.
Answer:-
Given:
- Areas of two similar triangles are 225 sq.cm. and 81 sq.cm.
- A side of the smaller triangle is 12 cm.
Using the theorem of areas of similar triangles, which states that “When two triangles are similar, the ratio of areas of those triangles is equal to the ratio of the squares of their corresponding sides”, we can find the corresponding side of the bigger triangle.
First, we have:
Area of bigger triangle / Area of smaller triangle = 225 / 81
Simplifying this expression, we get:
(Bigger triangle side)^2 / (Smaller triangle side)^2 = 15^2 / 9^2
Taking the square root of both sides, we get:
Bigger triangle side / Smaller triangle side = 15 / 9
Simplifying this expression, we get:
Bigger triangle side = (15/9) * 12
Solving this equation, we get:
Bigger triangle side = 20
Therefore, the corresponding side of the bigger triangle is 20 cm.
Chapter 1. Similarity- Practice Set 1.4 – Page 25
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