Question

If the areas of two similar triangles are in the ratio 16 is to 25 then find the ratio of their corresponding sides

Answer 1

ratio of the areas of two similar triangle

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= 16 : 25

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let the constant ratio be ' x '

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so now ,let the area of first triangle

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Ar1 = 16x cm^2

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area of second triangle

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Ar2 = 25x cm^2

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according to the property of similar triangle

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ratio of the corresponding sides of two similar ∆ will be

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= √( Ar1 / Ar2 )

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=√( 16x/ 25 x ) = √( 16/ 25 )

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= 4 / 5 = 4 : 5

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Answer:
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ratio of the corresponding sides = 4 : 5

Answer 2

Formula:

$\bigg( \dfrac{\text{Length 1}}{\text{Length 2}} \bigg)^2 = \dfrac{\text{Area 1}}{\text{Area 2}}$

Find the ratio of the sides:

$\bigg( \dfrac{\text{Length 1}}{\text{Length 2}} \bigg)^2 =\dfrac{16}{25}$

$\dfrac{\text{Length 1}}{\text{Length 2}} = \sqrt{\dfrac{16}{25} }$

$\dfrac{\text{Length 1}}{\text{Length 2}} =\dfrac{4}{5}$

Answer: The ratio is 4 : 5