Question

Adjacent sides of a rectangle are in the ratio 5 : 12, if the perimeter of the rectangle is 34 cm, find the length of the diagonal.

Answer 1

Adjacent sides i.e. Breadth and Length of a rectangle are in ratio 5:12.

Perimeter of rectangle is 34 cm.

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We have to find, Diagonal of Rectangle.

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We know that,

Length of Rectangle is always greater than Breadth.

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Therefore,

☯ Let the length of Rectangle be 12 x and Breadth be 5x.

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$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\tt\large{A}}\put(7.7,1){ \tt\large{B}}\put(9.5,0.7){\sf{\large{12x}}}\put(11.5,1){ \tt\large{C}}\put(8,1){\line(1,0){3.5}}\put(8,1){\line(0,2){2}}\put(11.5,1){\line(0,3){2}}\put(8,3){\line(3,0){3.5}}\put(11.6,2){\sf{\large{5x}}}\put(8.4,2){\sf{\large{Diagonal}}}\qbezier(8,1)(8,1)(11.5,3)\put(11.5,3){ \tt\large{D}}\put(11.3,1){\line(0,2){0.2}}\put(11.3,1.2){\line(2,0){0.2}}\end{picture}$

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$\underline{\bigstar\:\boldsymbol{According\:to\: Question\:}}$

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Perimeter of rectangle is 34 cm.

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We know that,

$\star\;{\boxed{\sf{\pink{Perimeter_{\;(Rectangle)} = 2(l + b)}}}}$

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$\dag\;{\underline{\frak{Putting\;values\;:}}}$

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$:\implies\sf 2(12x + 5x) = 34$

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$:\implies\sf 2(17x) = 34$

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$:\implies\sf 34x = 34$

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$:\implies\sf \cancel{ \dfrac{34}{34}}$

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$:\implies{\underline{\boxed{\sf{\pink{x = 1}}}}}\;\bigstar$

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Therefore,

• Length, 12x = 12 cm

• Breadth, 5x = 5 cm

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$\therefore$ Length and Breadth of Rectangle is 12 cm and 5 cm respectively.

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Now,

We have to find Diagonal of Rectangle,

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$\star\;{\boxed{\sf{\purple{D = \sqrt{ l^2 + b^2}}}}}$

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$\dag\;{\underline{\frak{Putting\;values\;:}}}$

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$:\implies\sf D = \sqrt{12^2 + 5^2}$

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$:\implies\sf D = \sqrt{144 + 25}$

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$:\implies\sf D = \sqrt{169}$

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$:\implies{\underline{\boxed{\sf{\purple{D = 13\;cm}}}}}\;\bigstar$

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$\therefore$ Hence, the diagonal of Rectangle is 13 cm.