Question 39

The area of a rectangle is equal to the area of a square whose diagonal is $$12\sqrt{6}$$ metre. The difference between the length and the breadth of the rectangle is 6 metre. What is the perimeter of rectangle ? (in metre).

Solution

Diagonal of square = $$12\sqrt{6}$$ m

=> Side of the square = $$\frac{diagonal}{\sqrt{2}} = \frac{12\sqrt{6}}{\sqrt{2}} = 12\sqrt{3}$$ m

=> Area of square = $$(12\sqrt{3})^2 = 432 m^2$$

Let length and breadth of the rectangle be $$l$$ and $$b$$

=> Area of rectangle = $$lb = 432$$

and $$l - b = 6$$

Solving above equations, we get $$l = 24$$ and $$b = 18$$

$$\therefore$$ Perimeter of rectangle = $$2 (l + b) = 2 (24 + 18)$$

= 2*42 = 84 m

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