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Congruence of Triangles

If ABC ∼ PQ...

Question

If $△ A B C \sim △ P Q R$ ,perimeter of $△ A B C = 32 c m$ ,perimeter of $△ P Q R = 48 c m$ and $P R = 6 c m$ ,find the length of $A C$ .

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Solution

Given:
△ABC∼△PQR,
perimeter of △ABC= 32cm,
perimeter of △PQR = 48cm and
PR = 6cm
since they are similar,
AB/PQ = BC/QR = AC/PR
AC/PR = perimeter of △ABC/perimeter of △PQR
AC/6 = 32/48
AC48 = 632
therefore AC = 4cm

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