Question

10. The width of a rectangle is 5
cm and its diagonal is 13 cm.
What is its perimeter ?​

Answer 1

☯ Let's consider that length of the rectangle be l.

Given that,

Width of the rectangle is 5 cm.

And, it's diagonal is 13 cm.

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$\underline{\boldsymbol{By \ using \ Pythagoras \ Theorem\: :}}$

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$:\implies\sf \Big(l \Big)^2 + \Big(5 \Big)^2 = \Big(13 \Big)^2 \\\\\\:\implies\sf l^2 + 25 = 169 \\\\\\:\implies\sf l^2 = 169 - 25 \\\\\\:\implies\sf l^2 = 144 \\\\\\:\implies\sf l = \sqrt{144} \\\\\\:\implies{\underline{\boxed{\frak{\purple{l = 12 \ cm}}}}}\:\bigstar$

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$\therefore\;{\underline{\sf{Here, \ measure \ of \ length \ is \ {\textsf{\textbf{12 cm}}}.}}}$

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⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\star\:\boxed{\sf{\pink{Perimeter_{\:(Rectangle)} = 2( Length + Breadth)}}}$

$:\implies\sf Perimeter_{\:(Rectangle)} = 2(12 + 5) \\\\\\:\implies\sf Perimeter_{\:(Rectangle)} = 2 \times 17 \\\\\\:\implies{\underline{\boxed{\frak{\purple{Perimeter_{\:(Rectangle)} = 34 \: cm}}}}}\:\bigstar$

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$\therefore\;{\underline{\sf{Hence, perimeter \ of \ the \ rectangle \ is \ {\textsf{\textbf{34 cm}}}.}}}$