Question

Q). If the Adjacent sides of a Rectangle are in the ration 5:12 and If the Perimeter of the Rectangle is 34 cm, Find the Length of the diagonals ? ​

Answer 1

Given : If the Adjacent sides of a Rectangle are in the ration 5:12 & If the Perimeter of the Rectangle is 34 cm.

To Find : Find the Length of the diagonals ?

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Solution : let the breadth and length of the rectangle be 5x & 12x.

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$\underline{\frak{As ~we ~know~ that~:}}$

• $\boxed{\sf\pink{Perimeter ~of~ rectangle~=~2\bigg(l~+~b\bigg)}}$

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$\qquad{\sf:\implies{2\bigg(l ~+~ b\bigg) ~= ~34cm}}$

$\qquad{\sf:\implies{2\bigg(12x ~+~ 5x\bigg) ~= ~34cm}}$

$\qquad{\sf:\implies{17x~=~\cancel\dfrac{34}{2}}}$

$\qquad{\sf:\implies{17x~=~17}}$

$\qquad{\sf:\implies{x~=~\cancel\dfrac{17}{17}}}$

$\qquad:\implies{\underline{\boxed{\frak{\purple{x~=~1}}}}}$★

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Therefore,

• Breadth = 5x => 5cm
• Length = 12x => 12cm

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$\underline{\frak{As ~we ~know~ that~:}}$

• $\underset{\blue{\bf Pythagoras\ Theorem}}{\underbrace{\boxed{\frak{\pink{Diagonal~=~\sqrt{(length^2~+~breadth^2)}}}}}}$

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$\qquad{\sf:\implies{Diagonal~=~\sqrt{(12^2~+~5^2)}}}$

$\qquad{\sf:\implies{Diagonal~=~\sqrt{(144~+~25)}}}$

$\qquad{\sf:\implies{Diagonal~=~\sqrt{169}}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{Diagonal~=~13m}}}}}$★

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Hence,

$\therefore\underline{\sf{The ~length ~of ~the ~diagonal~is~\bf{\underline{13m}}}}$