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

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Answer 1

Answer:

16

Step-by-step explanation:

as the triangle pqr and abc are similar then pqr/pq and abc/ab are also equal

then pqr/pq= abc/ab,

32/ab=24/12

then 32/ab=2

by changing side of 2 32/2=16

Answer 2

Answer:

AB = 16 cm

Step-by-step explanation:

Given:

• ∆ABC∼∆PQR
• Perimeter of ∆ ABC = 32 cm
• Perimeter of ∆ PQR = 24 cm
• PQ = 12 cm

To find:

Length of AB = ?

Solution:

When 2 triangles are similar, their corresponding sides would be equal.

∆ABC∼∆PQR

So,

$\sf{\dfrac{AB}{PQ} = \dfrac{BC}{QR} = \dfrac{AC}{PR} = \dfrac{Perimeter \: of \: \triangle ABC}{Perimeter \: of \: \triangle PQR} }$

Consider the part which is given and to find in the question.

$\implies \sf{ \dfrac{AB}{PQ} = \dfrac{Perimeter \: of \: \triangle ABC}{Perimeter \: of \: \triangle PQR} }$

$\implies \sf{ \dfrac{AB}{12} = \dfrac{32}{24} }$

$\implies \sf{AB = \dfrac{32 \times 12}{24} }$

$\implies \boxed{ \bf{AB = 16 \: cm} }$

∴ The length of AB = 16 cm