Question 142

The heights of two similar right-angled triangles ΔLMN and ΔOPQ are 48 cm and 36 cm. If OP = 12 cm, then LM is

Solution

ratio of heights of two similar triangles is always equal to the ratio of the corresponding sides of the triangles

i.e, $$\frac{\text{height of } \triangle LMN}{\text{height of } \triangle OPQ}$$ = $$\frac{\text{length of LM}}{\text{length of OP}}$$

put in values from the question

$$\frac{48}{36}$$ = $$\frac{\text{length of LM}}{12}$$

length of LM = 16

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