Question

find the area of rectangle whose side is 48 m and diagonal is 50 m​

Answer 1

Step-by-step explanation:

area of rectangle = L×B

therefore 48×50=

2400

Answer 2

$\star$ᴅɪᴀɢʀᴀᴍ

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$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,2.74){\framebox(0.25,0.25)}\put(4.74,0.01){\framebox(0.25,0.25)}\put(2,-0.7){\sf\large 48m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\qbezier(0,0)(0,0)(5,3)\put(1.65,1.8){\sf\large 50 m}\put(5.5,1.5){\sf\large 14m}\end{picture}$⠀

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$\frak{Given}\begin{cases}\sf{\:\;\:One \: side_{\:(rectangle)} = 48 \: m}\\\sf{\:\:\: Diagonal_{\:(rectangle)} = 50\: m}\end{cases}$

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❒ Let ABCD be the rectangle. Then,

• AB = 48 m
• AC = 50 m

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Now, In ∆ABC

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$\bigstar\:{\underline{\sf{Using\; Pythagoras\; Theroem\;\::}}}$

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$:\implies\sf AC^2 = AB^2 + BC^2 \\\\\\:\implies\sf 50^2 = 48^2 + BC^2 \\\\\\:\implies\sf BC^2 = 50^2 - 48^2 \\\\\\:\implies\sf BC^2 = 2500 - 2304 \\\\\\:\implies\sf BC^2 = 196 \\\\\\:\implies\sf BC = \sqrt{196} \\\\\\:\implies{\underline{\boxed{\sf{\pink{BC = 14 \: m}}}}}\:\bigstar$

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$\therefore\;{\underline{\sf{Here, \: we \: get \: BC \:is\; \bf{14 \: cm}.}}}$

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

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$\bf{\dag}\quad\large\boxed{\sf Area_{\: (rectangle)} = Length \times Breadth }$

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$\bf{Here}\begin{cases}\sf{\:\:\: Length_{\:(rectangle)} = 48 \: m}\\\sf{\:\:\; Breadth_{\:(rectangle)} = 14 \: m}\end{cases}$

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Therefore,

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$:\implies\sf Area_{\:(rectangle)} = 48 \times 14 \\\\\\:\implies{\underline{\boxed{\frak{\purple{672\:m^2}}}}}\:\bigstar$

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$\therefore\;{\underline{\sf{Hence,\;area\:of\: rectangle\:is\; \bf{672\;m^2}.}}}$