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The perimeters of two similar triangles ABC and LMN are 120 cm and 96 cm respectively. If LM = 16 cm, then the length of AB is :

  1. 20 cm

  2. 16 cm

  3. 15 cm

  4. 12 cm

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Answer

The two similar triangles ABC and LMN are shown in the figure below:

The perimeters of two similar triangles ABC and LMN are 120 cm and 96 cm respectively. If LM = 16 cm, then the length of AB is : 1. 20 cm 2. 16 cm 3. 15 cm 4. 12 cm. Model Paper 4, Concise Mathematics Solutions ICSE Class 10.

We know that,

If two triangles are similar then the ratio of their perimeter is equal to the ratio of their corresponding sides.

⇒Perimeter of △ABCPerimeter of △LMN=ABLM⇒12096=AB16⇒AB=120×1696⇒AB=20 cm.\Rightarrow \dfrac{\text{Perimeter of △ABC}}{\text{Perimeter of △LMN}} = \dfrac{AB}{LM} \\[1em] \Rightarrow \dfrac{120}{96} = \dfrac{AB}{16} \\[1em] \Rightarrow AB = \dfrac{120 \times 16}{96} \\[1em] \Rightarrow AB = 20 \text{ cm}.

Hence, Option 1 is the correct option.

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