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

Answer:

premiter of rectangle=2(l+b)

$2(5x + 12x) = 34 \\ 2 \times (17x) = 34 \\ 17 x= \frac{34}{2} \\ 17 x= 17 \\ x= 1$

so L=12,B=5

length of diagonal=

${d}^{2} = {l}^{2} + {b}^{2} \\ {d}^{2} = {12}^{2} + {5}^{2} \\ {d}^{2} = 144 + 25 \\ {d }^{2} = 169 \\ d = 13$

Answer 2

Given: The adjacent sides of a rectangle are in the ratio of 5 : 12. & The perimeter of the rectangle is 34 cm.

Need to find: The Length and Diagonal?

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❍ Let's say, that the Length and Breadth of the given rectangle be 5x and 12x respectively.

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

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$\star\;\underline{\boxed{\pmb{\sf{Perimeter_{\:(rectangle)} = 2(Length + Breadth)}}}}$

$\sf{We \;have}\begin{cases}\sf{\quad Length = \bf{5x}}\\\sf{\quad Breadth = \bf{12x}}\\\sf{\quad Perimeter =\bf{34\; cm}}\end{cases}$

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

$:\implies\sf 34 = 2 \times 17x$

$:\implies\sf 34 = 34x$

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

$:\implies\underline{\boxed{\pmb{\frak{x = 1}}}}\;\bigstar$

Therefore,

• Length of the rectangle, 5x = 5(1) = 5 cm
• Breadth of the rectangle, 12x = 12(1) = 12 cm

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$\therefore{\underline{\textsf{Hence, the Length and Breadth of rectangle are \textbf{5, 12 cm} respectively.}}}$

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✇ Now, we've to find out the Diagonal of the rectangle. & To Calculate the Diagonal of rectangle formula is Given by —

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$\star\:\underline{\boxed{\pmb{\sf{Diagonal_{\:(rectangle)} = \sqrt{\Big(Length\Big)^2 + \Big( Breadth\Big)^2}}}}}$

» Substituting the Values in the formula —

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$:\implies\sf Diagonal_{\:(rectangle)} = \sqrt{(5)^2 + (12)^2}$

$:\implies\sf Diagonal_{\:(rectangle)} = \sqrt{25 + 144}$

$:\implies\sf Diagonal_{\:(rectangle)} = \sqrt{169}$

$:\implies{ \pmb{\underline{\boxed{\frak{ \mathsf{D}iagonal_{\:(rectangle)} = 13}}}}}\;\bigstar$

$\therefore{\underline{\textsf{Hence, the Diagonal of the rectangle is \textbf{13 cm}.}}}$