Question

1. The length of a field exceeds its breadth by 3
meters. If the length is increased by 3 meters
and breadth is decreased by 2 meters. The
area remains the same. What are the length
and breadth respectively of the field?
(a) 15 m, 12 m
(b) 12 m, 15 m
(c) 18 m, 10 m
(d) 10 m, 18 m​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

Answer is (a) 15m, 12m

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

Let us consider the breadth of the field as x

Length exceeds breadth by 3 m

Exceeds means more than

Length of the field = 3 m more than breadth = 3 m more than x = (x + 3)

$\boxed{\tt{Area\:of\: Rectangle= Length \times Breadth}}$

Area of the field = x(x + 3) = (x² + 3x) m²

Length of the field when original length increased by 3 m = x + 3 + 3 = (x + 6) m

Breadth of the field when original breadth decreased by 2 m = (x - 2) m

$\boxed{\tt{Area\:of\: Rectangle= Length \times Breadth}}$

Area of field when original length increased by 3 m and when original breadth decreased by 2 m = (x + 6)(x - 2)

= x(x - 2) + 6(x - 2)

= x² - 2x + 6x - 12

= x² + 4x - 12

So Area of field when original length increased by 3 m and when original breadth decreased by 2 m = (x² + 4x - 12) m²

Given area remains same when length is increased and breadth is decreased

So, Area of the field = Area of field when original length increased by 3 m and when original breadth decreased by 2 m

So equation formed :

${x}^{2} + 3x = {x}^{2} + 4x - 12$

${x}^{2} - {x}^{2} + 3x - 4x = - 12$

$- x = - 12$

$x = - ( - 12)$

$x = 12$

So Breadth = x = 12 m

Length = (x + 3) = (12 + 3) = 15 m