Question

school is organising a competition in which a child has to make a painting whose perimeter is 60cm. area is decreased by 11 cm sq. length is decreased by 3cm and breadth is increased by 2cm find the dimensions

Answer 1

Since the question talks of length and breadth hence painting is rectangular in shape.

Let the legth of rectangle be L cm

Let the breadth of rectangle be b cm

Perimeter, P = 60cm

2L + 2b = 60 – ( 1 )

According to question

( L × b ) – 11 = ( L – 3 ) × ( b + 2 )

Lb – 11 = Lb + 2L – 3b – 6

– 11 + 6 = 2L – 3b

2L – 3b = –5. – (2 )

Now,

2L + 2b = 60 – ( 1 )

2L – 3b = –5 – (2 )

_(–)_(+)____(+)__-

5b = 65

b = 65 / 5

b = 13 cm

Put b in eq ( 1 )

2L + 2(13) = 60

2L = 60 – 26

2L = 34

L = 34 / 2

L = 17 cm

Hope the solution is clear to you!!