Question

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

Answer 1

Answer:

16cm is the correct answer.

The perimeter and sides are in proportion as the triangles are similar.

Answer 2

Given that :- ΔABC ∼ ΔPQR,

Perimeter of ΔABC$= AB + BC + AC = 32 cm$

Perimeter of ΔPQR $= PQ + QR + RP = 24 cm$

and $PQ = 12 cm$

As we have to find AB,

Now,

$\frac{AB}{PQ} =\frac{BC}{QR} =\frac{CA}{RP}$

$=\frac{AB + BC + CA}{PQ + QR + RP} = \frac{32}{24}$

Therefore,

$\frac{AB}{12}=\frac{32}{24}$

$AB = \frac{384}{24}$

$AB = 16 cm$