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 168cm2
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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