Question

the breadth of the rectangle is 3 less than the lenght of the rectangle.If the length is increased by 9 cm. and breadth is diminished by 5 cm. the area remains unaltered. find the dimensions of the rectangle

Answer 1

Let the length of the rectangle be x. Therefore the breadth will be (x-3) since breadth is 3 less than the length. Therefore the area of the rectangle is x(x-3) = x²-3x.
Now the new length and breadth are (x+9) and (x-3-5)= (x-8). Therefore area = (x+9)(x-8) = x²+x+72.
Since, x²-3x = x²+x+72, solving the equations we get x = 18.
Therefore the length is 18 and breadth is 18-3 = 15.