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SSS Similarity

The perimeter...

Question

The perimeter of 2 similar triangles ABC and LMC are 60 cm and 48 cm respectively. If AB = 10 cm, Find LM.

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Solution

Perimeter of triangle $A B C = 60$ cm
Perimeter of triangle $L M C = 48$ cm

$A B = 10$ cm
$L M = ?$ cm

In similar triangles $A B C & L M C,$
ratios of perimeters of the triangles are equal to the ratios of their respective sides.

$\frac{p e r i m e t e r o f t r i a n g l e A B C}{p e r i m e t e r o f t r i a n g l e L M C} = \frac{A B}{L M}$

$\frac{60}{48} = \frac{10}{L M}$

$L M = \frac{10 \times 48}{60}$

$L M = 8$ cm

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A B C

L M N

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48 c m

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A B

The perimeters of two similar triangles ABC and PQR are respectively 36 cm and 24 cm. If PQ = 10 cm, find AB.

△ A B C

△ D E F

36

24

D E = 10

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△ A B C ≅ △ D E F

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