The area of a rectangle is equal to the area of a square whose diagona

1.	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).1). 160 metre2). 80 metre3). 82 metre4). 84 metre
Answer» 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

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).1). 160 metre2). 80 metre3). 82 metre4). 84 metre

Answer»

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