Question

the length of a field exceeds its breadth by 5m . if the breadth be increased by 12m and length is decrease by 5m, then the area of the field is increased by 140msquare find the length and breadth of the field

Answer 1

Let the breadth of the rectangle be x.

Then length will be x+5

Formula for Area of rectangle = length × breadth

Area = $\rm (x+5) \times x = (x+5)x$

Now if breadth is increased by 12m and length is decreased by 5, the area is increased by 140m².

Therefore, we can conclude,

$\rm \implies [(x+5)-5](x+12) = (x+5)x + 140m^2$

$\rm \implies (x+5-5)(x+12) = x^2+5x+ 140m^2$

$\rm \implies x(x+12) = x^2+5x + 140m^2$

$\rm \implies x^2 + 12x = x^2+5x + 140m^2$

Same terms present on both the sides of the equation will be cancelled

$\rm \implies 12x =5x + 140m^2$

$\rm \implies 12x -5x =140m^2$

$\rm \implies 7x =140m^2$

$\rm \implies x = \dfrac{140}{7} = 20$

$\therefore \qquad \rm Breadth = x = 20m$

$\qquad \ \ \rm Length = x +5 = 20m+5m = 25m$

Therefore, the length and breadth of the field are 25m and 20m respectively.

Hope it helps