Question

the ratio of the areas of a square and a rectangle of length 4 cm and breadth 3 cm is 4 : 3. the side of the square will be​

Answer 1

$\sf Given \begin{cases} & \sf{Length\:of\:rectangle = \bf{4\:cm}} \\ & \sf{Breadth\:of\:rectangle = \bf{3\:cm}} \\ & \sf{Area_{\;(square)} : Area_{\:(rectangle)} = \bf{4:3}} \end{cases}$

To find: Length of side of square?

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⋆ Perimeter of Rectangle is given by,

$\star\;{\boxed{\sf{\pink{Area_{\;(rectangle)} = Length \times Breadth}}}}$

$:\implies\sf Area_{\;(rectangle)} = l \times b$

Here,

l = 4 cm

b = 3 cm

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$:\implies\sf Area_{\;(rectangle)} = 4 \times 3\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{Area_{\;(rectangle)} = 12\:cm^2}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Area\:of\:rectangle\:is\: \bf{12\:cm^2}.}}}$

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☯ Let length of sides of square be x cm.

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$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

$\sf Area\:of\:square : Area\:of\:rectangle = 4:3$

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$:\implies\sf (side \times side) : (length \times breadth) = 4 : 3\\ \\ \\:\implies\sf x^2 : 12 = 4 : 3\\ \\ \\:\implies\sf \dfrac{x^2}{12} = \dfrac{4}{3}\\ \\ \\ :\implies\sf x^2 = \dfrac{4}{3} \times 12\\ \\ \\ :\implies\sf x^2 = \cancel{\dfrac{48}{3}}\\ \\ \\ :\implies\sf x^2 = 16\\ \\ \\ :\implies\sf \sqrt{x^2} = \sqrt{16}\\ \\ \\ :\implies\sf x = \sqrt{16}\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{x = 4}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Thus,\:the\; length\:of\:sides\:of\:square\:is\: {\textsf{\textbf{4\:cm}}}.}}}$

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$\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

$\sf Perimeter\:of\:rectangle = \bf{2(length + breadth)}$

$\sf Diagonal\:of\:rectangle = \bf{\sqrt{(length)^2 + (breadth)^2}}$

$\sf Perimeter\:of\:square = \bf{4 \times side}$

$\sf Diagonal\:of\:square = \bf{\sqrt{2} \times side}$

Answer 2

Let area of square be x

Area of triangle 4*3 = 12 sq. cm

Area a square: Area of a triangle = 4:3

x : 12 = 4:3

3x = 12*4

3x = 48

x = 16

Area of square is 16 sq cm.