Question

If diagonal of a rectangle is 20 cm and one side is 16 cm,find the other side​

Answer 1

Given : Diagonal of a rectangle is 20cm and one side is 16cm

To Find : Other side.

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

• According to the Pythagoras theorem, the square hypotenuse is equal to the sum of squares of perpendicular and base of the triangle.

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$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,2.74){\framebox(0.25,0.25)}\put(4.74,0.01){\framebox(0.25,0.25)}\put(2,-0.7){\sf\large 16cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\qbezier(0,0)(0,0)(5,3)\put(1.65,1.8){\sf\large 20cm}\end{picture}$

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$\sf \: In \: right \: \triangle \: ABC,$

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$\sf : \implies\: AC {}^{2} = AB {}^{2} + BC {}^{2}$

$\:$

$\sf : \implies \: (20) {}^{2} = (16) {}^{2} + BC {}^{2}$

$\:$

$\sf : \implies \: 400 = 256 + BC {}^{2}$

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$\sf : \implies \: BC {}^{2} = 400 - 256$

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$\sf : \implies \: BC {}^{2} = 144$

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$\sf : \implies \: BC = \sqrt{144}$

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$\sf : \implies \: \bold{ BC = 12 \: cm}$

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$\sf\therefore{\underline{Hence, \: the \: other \: side \: is \: \bold{12 \: cm}.}}$

Answer 2

$\sf : \implies\: AC {}^{2} = AB {}^{2} + BC {}^{2}$

$\sf : \implies \: (20) {}^{2} = (16) {}^{2} + BC {}^{2}$

$\sf : \implies \: 400 = 256 + BC {}^{2}$

$\sf : \implies \: BC {}^{2} = 400 - 256$

$\sf : \implies \: BC {}^{2} = 144$

$\sf : \implies \: BC = \sqrt{144}$

$\sf : \implies \: \bold{ BC = 12 \: cm}$

$\sf\therefore{\underline{Hence, \: the \: other \: side \: is \: \bold{12 \: cm}}}$