Question

the perimeter of a rectangle is 240 CM if the length is decreased by 10% and the breadth is increased by 20% will get the same perimeter find the original length and breadth of the rectangle

Answer 1

Perimeter of a rectangle = 2(l+b)
2(l+b) = 240
⇒ (l+b)= 120 →(1)
If the length is decreased by 10 % then the new length is  l- 10%of l
= (100l -10)/100 = 9/10 l
If the breadth is increased by 20% then the new breadth is b+20% of b
= (100b+20)/100 = 12/10 b
according to the qstn
2(9/10l+12/10b) = 240
9/10l + 12/10b = 120 → (2)

Solving (1) and (2)
 (l+b)= (910l+ 12/10b)

⇒l= 2b
l-2b = 0 → (3)
Subtracting (3) from (1)
(l+b)-(l-2b) = 120 -0
l+b-l+2b = 120
3b = 120
⇒b = 40cm
Substituting the value of b in (1)
we get l = 80cm
∴ length of the triangle is 80cm and breadth is 40 cm...




Hope it helps...:)