Question

14. The length of a rectangle exceds the breadth by 6 cm. If the length is increased by 3 cm
and breadth is decreased by 2 cm, the the area remains same. Find the length and breadth of
the rectangle​

Answer 1

Answer:

Length = 24 cm Breadth = 18 cm

Step-by-step explanation:

Let Length of rectangle be x and Breadth of rectangle be y

then,

         x = y + 6 (Length is 6 more than breadth)

Area of rectangle = xy = (y+6)(y) = y^2 + 6y

Case 2

          Length increased by 3 = x + 3

          Breadth decreased by 2 = y - 2

Area = (x+3)(y-2) = (y+6+3)(y-2)  =  y^2 + 7y - 18

Area in Both cases are equal

y^2 + 6y = y^2 + 7y - 18

from here

-y = -18

y=18

As x = y+6

x = 24

Length = 24 cm

Breadth = 18 cm

Answer 2

Answer :

Let length of the rectangle be L then the breadth of the rectangle is (L-6) So the area of the rectangle is L(L-6) Now length is increased by 3cm so new length is (L+3) and breadth is decreased by 2 cm so new breadth is (L-8) Hence new area is (L+3)*(L-8) So new area is L^2 -5L-24 is same as Area . L^2-6L =>L^2-5L-24 =>

length and breadth of the rectangle are 24 cm and 18 cm .