Question

the length of a rectangle is twice its breadth. if its diagonals is 4/5cm , find the perimeter of the rectangle

Answer 1

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Here is your answer

Let breadth be x

So, length = 2x
Diagonal = $\frac {4}{5}cm$

${ (\frac{4}{5}) }^{2} = (2x) {}^{2} + (x) {}^{2} \\ \\ \frac{16}{25} = 4 {x}^{2} + {x}^{2} \\ \\ \frac{16}{25} = 5 {x}^{2} \\ \\ {x}^{2} = \frac{16}{25 \times 5} \\ \\ x = \frac{4}{5 \sqrt{5} }$
So,

$breadth = \frac{4}{5 \sqrt{5} }$
Now,

$length = \frac{4}{5 \sqrt{5} } \times 2 \\ \\ = \frac{8}{5 \sqrt{5} }$
Perimeter = 2(l + b)

$= 2( \frac{8}{5 \sqrt{5}} + \frac{4}{5 \sqrt{5} } ) \\ \\ = 2 \times \frac{12}{5 \sqrt{5} } \\ \\ = \frac{24}{5 \sqrt{5} }$
Therefore,

$perimeter = \frac{24}{5 \sqrt{5} }$


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