Question

School organized a competition in which a child has to make a painting whose
perimeter is 60cm. Its area will be decreased by 11 sq.cm, if its length is decreased by
3cm and breadth is increased by 2cm then find the dimensions of the painting?​

Answer 1

Step-by-step explanation:

Let the length be x. And the breadth be y.

(x - 3)(y + 2) = xy - 11

xy + 2x - 3y -6 = xy -11

xy + 2x - 3y = xy - 11 + 6

xy + 2x - 3y = xy - 5

2x - 3y = xy - xy - 5

2x - 3y = -5 ..........(I)

2(x + y) = 60

x + y = 30 ...........(ii)

Solving (I) and (II) simultaneously we get

2x - 3y + x + y = 30 - 5

3x - 2y = 25

3x - 2y + x + y = 25 + 30

4x - y = 55

4x - y + x + y = 55 + 30

5x = 85

x = 17

x + y = 30

17 + y = 30

y = 13

Length is 17 and the breadth is 13.