Question

The areas of two similar triangles abc and def are 256 cm2 and 144 cm2 respectively. Of the longest side of the larger triangle abc be 32 cm, find the longest side of the smaller triangle

Answer 1

Answer:

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Answer 2

The longest side of the smaller triangle is 21 cm

Step-by-step explanation:

Theorem : The ratio of square of the corresponding sides of similar triangles is equal to the ratio of the area of the corresponding triangles .

The areas of two similar triangles abc and def are 256 sq.cm. and 144 sq.cm

Of the longest side of the larger triangle abc be 32 cm

Now to find the longest side of the smaller triangle

Let the longest side of the smaller triangle be x

Using theorem :

$\frac{32^2}{x^2}=\frac{256}{144}\\\\\frac{32^2 \times 144}{256}=x^2\\576=x^2\\\sqrt{576}=x\\24=x$

Hence the longest side of the smaller triangle is 21 cm

#Learn more:

The areas of two similar triangles abc and def are 144 cm2 and 81 cm2 , respectively. if the longest side of larger abc be 36 cm, then find the longest side of the similar triangle def

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