Question

The length of rectangle is 1cm less the twice its breadth. If its area is 66 sq.cm, then find the length, breadth and perimeter of the rectangle​

Answer 1

Answer:

6 cm, 11cm and 34 cm

Step-by-step explanation:

Let the breadth of the rectangle be b cm,

Then, ATQ, Length becomes 2b - 1

$ar(rectangle) = lb = 66 cm^2\\(b)(2b-1) = 66\\2b^2 - b = 66\\2b^2 - b - 66 = 0\\2b^2 - 12b + 11b - 66 = 0\\2b (b - 6) + 11( b - 6) = 0\\(2b + 11) (b - 6) = 0\\(i) Either (2b + 11) = 0\\or (ii) (b - 6) = 0$

(ii) (2b + 11) = 0 or b = -11/2 is not possible

while (i) gives b = 6 cm which is the only possible solution

$l = 2b - 1\\= 2(6) - 1\\= 11 cm\\and\\Perimeter = 2(l + b)\\= 2(11 + 6)\\= 2(17)\\= 34 cm$