Question

The breadth of a rectangle is 3 less than the length of the rectangle. If the length is increased by 9cm and breadth is diminished by 5cm, the area remains unaltered. Find the dimensions of the rectangle.​

Answer 1

Answer:

the answer is length = 18cm, breadth =15cm

Step-by-step explanation:

the breadth of the rectangle is 3 less than length of the rectangle.

Let the length of rectangle be x

Now the breadth will become = x-3

Now calculating the area of rectangle

$area \: of \: rectangle \: = length \: \times breadth \\ = x \times (x - 3) \\ = {x}^{2} - 3x$

Now the length is increased by 9cm and breadth is diminished or decreased by 5cm and the area remains unaltered i.e. unchanged

therefore the new length = x+9

new breadth = (x-3) -5

= x-3-5 = x-8

now calculating the area of rectangle according to new length and breadth.

$area \: of \: rectangle \: = length \: \times breadth \\ = (x + 9) \times (x - 8) \\ = {x}^{2} - 8x + 9x - 72 \\ = {x}^{2} + x - 72$

Now equating the two areas we will get,

${x}^{2} - 3x = {x}^{2} + x - 72 \\ {x }^{2} - {x}^{2} = 3x + x - 72 \\ 0 = 4x - 72 \\ 4x = 72 \\ x = \frac{72}{4} = 18cm$

therefore the length of rectangle is 18cm

and breadth of original rectangle is = 18 - 3 = 15cm

Answer 2

$Area \: of \: Rectangle = l×b$

$= (x + 9) \times (x - 8)$

$= {x}^{2} - 8x + 9x - 72$

$= {x}^{2} + x - 72$

$Both \: Areas \: are :$

${x}^{2} - 3x = {x}^{2} + x - 72$

${x}^{2} - {x}^{2} = 3x + x - 72$

$0 = 4x - 72$

$x = \frac{72}{4}$

$x = 18$

$l = 18$

$b = 18 - 3 = 15$