Two triangles are similar and the ratio of their corresponding sides is 3:5. If the area of the smaller triangle is 45 cm², what is the area of the larger triangle?

hard 4 marks Class 6 · Mathematics · Understanding Elementary Shapes

Answer

125 cm²

The correct answer is 125 cm² — Multiply the smaller area by this factor: $45 \times \frac{25}{9} = 5 \times 25 = 125$ . Thus the larger triangle’s area is $125$ cm².

Step-by-step solution

The side ratio between the triangles is $\frac{5}{3}$ . Area scales with the square of the linear ratio. Compute $(\frac{5}{3})^{2} = \frac{25}{9}$ .
Multiply the smaller area by this factor: $45 \times \frac{25}{9} = 5 \times 25 = 125$ . Thus the larger triangle’s area is $125$ cm².

Common mistake: Applying the linear side ratio directly to the area instead of squaring it

Concept tested: Similarity of triangles and area scaling

Published 7 October 2026 · How this solution was prepared and checked

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