(A) Let the side of the square be $x\,cm$.According to the problem:Area of the rectangle $= 3 \times$ Area of the squareThe length of the rectangle is

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(A) Let the side of the square be $x\,cm$.According to the problem:Area of the rectangle $= 3 \times$ Area of the squareThe length of the rectangle is $20\,cm$ and the breadth is $\frac{3}{2}x$.So,Area of the rectangle $= 20 \times \frac{3}{2}x = 30x$.Area of the square $= x^2$.Equating the areas:$30x = 3 \times x^2$Dividing both sides by $3x$ (since $x \neq 0$):$10 = x$Therefore,the side of the square is $10\,cm$.

Competitive Quantitative Aptitude Mensuration Measurement of Area

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The area of a rectangle is thrice that of a square. The length of the rectangle is $20\,cm$ and the breadth of the rectangle is $\frac{3}{2}$ times that of the side of the square. The side of the square (in $cm$) is

A
$10$
B
$20$
C
$30$
D
$60$

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The area of a rectangle is thrice that of a square. The length of the rectangle is $20\,cm$ and the breadth of the rectangle is $\frac{3}{2}$ times that of the side of the square. The side of the square (in $cm$) is

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What is the area of a given right-angled triangle?
$I.$ The length of the hypotenuse is $5\, cm$.
$II.$ The perimeter of the triangle is four times that of its base.
$III.$ One of the angles of the triangle is $60^{\circ}$.