# The length of a rectangle is greater than the breadth by 18cm. If both length and breadth are increased by 6 cm, then area increases by 168cm square. Find the length and breadth of the rectangle

**Given :** The length of a rectangle is greater than the breadth by 18cm.
If both length and breadth are increased by 6cm , then area is increases by 168cm^{2}

**To do:** Find the breadth of the rectangle

**Solution**
Let the breadth of the rectangle = x cm

Length of the rectangle = $x + 18$ cm

Area of the rectangle = $L \times B = (x + 18) . x$

=$ x(x+ 18)$

length and breadth increased by 6cm each and area increases by 168 sq cm

$(x + 18 + 6)(x + 6) = x(x + 18) + 168$

$(x + 24)(x + 6)= x^2 + 18x + 168$

$x^2 + 30x + 144 = x^2 + 18x + 168$

$30x - 18x = 12x = 168 - 144 = 24$

$12x = 24$

$x = \frac{24}{12} = 2; x = 2$

**So length and breadth of the rectangle are**

**2 + 18, 2 or 20 cm and 2 cm respectively**

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