Question

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

Answer 1

$\huge\underline\bold\color{red}\mathfrak{Answer}$

Area of square = a²

Area of rectangle = lb

We know the length and breadth of the rectangle. So we find its area.

Area = lb = 4×3 = 12 cm²

Now we know the ratio of the area of square and rectangle is 4:3

ie, a² : 12 = 4 : 3

a²/12 = 4/3

a² = 12×4/3

a² = 16

a = √16

a = 4 cm

Side of the square is 4 cm.

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Answer 2

$\:\:\:\dag\:{\underline{\underline{\mathfrak{\red{Given:-}}}}}$

• $\textsf{Length of rectangle = 4cm}$

• $\textsf{Breadth of rectangle = 3cm}$

• $\sf{Area_{(square)} : Area_{(rectangle)} = 4:3}$

$\:\:\:\dag\:{\underline{\underline{\mathfrak{\orange{To\: Find:-}}}}}$

• $\textsf{Length of side of square}$

$\:\:\:\dag\:{\underline{\underline{\mathfrak{\blue{Solution:-}}}}}$

$\bigstar\:\:{\underline{\boxed{\sf{\purple{Area_{(rectangle)} = Length \times Breadth}}}}}$

$\:\:\::\implies\:\:\sf{Area_{(rectangle)} = 4 \times 3}$

$\:\:\::\implies\:\:\sf{Area_{(rectangle)} = 12cm^{2}}$

$\bigstar\:\:{\underline{\boxed{\sf{\purple{Area_{(square)} : Area_{(rectangle)} = 4 : 3}}}}}$

$\:\:\::\implies\:\:\sf{(side \times side) : (length\times breadth) = 4:3}$

$\:\:\::\implies\:\:\sf{x^{2} : 12 = 4 : 3}$

$\:\:\::\implies\:\:\sf{\dfrac{x^2}{12} = \dfrac{4}{3}}$

$\:\:\::\implies\:\:\sf{x^{2} = \dfrac{4}{3} \times 12}$

$\:\:\::\implies\:\:\sf{x^2 = \dfrac{48}{3}}$

$\:\:\::\implies\:\:\sf{x^2 = 16}$

$\:\:\::\implies\:\:\sf{\sqrt{x^2} = \sqrt{16}}$

$\:\:\::\implies\:\:\sf{x = \sqrt{16}}$

$\:\:\::\implies\:\:{\underline{\boxed{\mathfrak{\pink{x = 4\:cm}}}}}$