Question

5) The perimeters of two similar triangles ABC and PQR are 32 cm and
24 cm respectively. If PQ = 12 cm, find AB.​

Answer 1

Step-by-step explanation:

The ratio of the areas of two similar triangles is equal to the squares of the ratios of their perimeters and is also equal to the squares of the ratos of their corresponding sides.

Hence,

$\because \: \triangle ABC \sim \triangle PQR\\ \therefore \: ( { \frac{32}{24} )}^{2} = ( \frac{AB }{PQ} )^{2} \\ \therefore \: \frac{32}{24} = \frac{AB }{PQ} \: \\ \frac{32}{24} = \frac{AB }{12} \\ AB = \frac{32 \times 12}{24} \\ AB = 16 \: cm$