Question

Four circles have areas in the ratio 3 : 7 : 11 : 19 . Four squares are formed whose diagonals are proportional to the radii of the above circles. find the proportional of the areas of the squares so formed.​

Answer 1

$\underline{\boxed{\bold{Question}}}$

• Four circles have areas in the ratio 3 : 7 : 11 : 19 . Four squares are formed whose diagonals are proportional to the radii of the above circles. find the proportional of the areas of the squares so formed.

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$\underline{\boxed{\bold{Given}}}$

• Ratio of diagonals = 3 : 7 : 11 : 19

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$\underline{\boxed{\bold{Answer}}}$

Lets start !

Let's assume as follows

→ Diagonal of square S₁ = 3k

→ Diagonal of square S₂ = 7k

→ Diagonal of square S₃ = 11k

→ Diagonal of square S₄ = 19k

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Area of square if length of diagonal is "M" is given by :

$\underline{\boxed{\bold{Area\;of\;square = \frac{1}{2}M^2 }}}$

$\bold{\therefore Area\;of\;square\; S_{1} = A_{1} = \frac{1}{2}(3k)^2= \frac{9k^2}{2} }$

$\bold{\therefore Area\;of\;square\; S_{2}= A_{2} = \frac{1}{2}(7k)^2= \frac{49k^2}{2} }$

$\bold{\therefore Area\;of\;square\; S_{3}=A_{3} = \frac{1}{2}(11k)^2= \frac{121k^2}{2} }$

$\bold{\therefore Area\;of\;square\; S_{4}= A_{4}= \frac{1}{2}(19k)^2= \frac{361k^2}{2} }$

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So ratio of their areas is given by

A₁ : A₂ : A₃ : A₄ = 9 : 49 : 121 : 361

$\boxed{\boxed{\bold{\therefore Ratio \; of \;area\;of \;square = 9:49:121:361}}}$

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Refer the given link for clarification

Area of square if diagonals are given.

https://brainly.in/question/20315755

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Hope this helps u.../

【Brainly Advisor】

Answer 2

Answer:

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