Question : $\Delta ABC$ and $\Delta DEF$ are two similar triangles and the perimeters of $\Delta ABC$ and $\Delta DEF$ are 90 cm and 54 cm respectively. If the length of DE = 36 cm, then the length of AB is:
Option 1: 60 cm
Option 2: 40 cm
Option 3: 45 cm
Option 4: 50 cm
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Correct Answer: 60 cm
Solution : The ratio of the perimeters of two similar triangles is equal to the ratio of their corresponding sides. $\frac{{AB}}{DE} = \frac{\text{Perimeter of $\Delta ABC$}}{\text{Perimeter of $\Delta DEF$}}$ ⇒ $\frac{AB}{36\;cm} = \frac{90\;cm}{54\;cm}$ ⇒ AB = 60 cm Hence, the correct answer is 60 cm.
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Question : The areas of two similar triangles $\Delta ABC$ and $\Delta PQR$ are 36 sq. cm and 9 sq. cm, respectively. If $PQ$ = 4 cm, then what is the length of $AB$ (in cm)?
Option 1: 16 cm
Option 2: 12 cm
Option 3: 8 cm
Option 4: 6 cm
Question : $\triangle ABC \sim \triangle DEF$ and the perimeters of $\triangle ABC$ and $\triangle DEF$ are 40 cm and 12 cm respectively. If DE = 6 cm then AB is:
Option 1: 12.6 cm
Option 2: 24 cm
Option 3: 20 cm
Option 4: 10 cm
Question : $\triangle \mathrm{ABC} \sim \triangle \mathrm{DEF}$ and the perimeters of these triangles are 32 cm and 12 cm, respectively. If $\mathrm{DE}=6 \mathrm{~cm}$, then what will be the length of AB?
Option 2: 14 cm
Option 3: 12 cm
Option 4: 18 cm
Question : The perimeter of two similar triangles $\Delta \mathrm{ABC}$ and $\Delta\mathrm{ PQR}$ are $60\;\mathrm{cm}$ and $36\;\mathrm{cm}$ respectively. If $\mathrm{PQ} = 18\;\mathrm{ cm}$, then $\mathrm{AB}$ is:
Option 1: $20\;\mathrm{cm}$
Option 2: $24\;\mathrm{cm}$
Option 3: $36\;\mathrm{cm}$
Option 4: $30\;\mathrm{cm}$
Question : The perimeter of two similar triangles ABC and PQR are 36 cm and 24 cm respectively. If PQ = 10 cm. then the length of AB is:
Option 1: 18 cm
Option 3: 15 cm
Option 4: 30 cm
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