Question

If length and breadth of metal sheet are increased by 1% each. Then find percentage change in its perimeter.
Options:
increases by 1%
increases by 2%
increases by 4%
None of these​

Answer 1

Let the initial,

Length = l

Breadth = b

∴ Perimeter = 2(l + b)

Finally,

Length = 1% of l + l

⇒l′ = 1/100 × l + l

⇒l′ = l/100 + l

⇒l′ = (l + 100l)/100 = 101l/100 = 1.01 l

Breadth = 1% of b + b

⇒b′ = 1/100 × b + b

⇒b′ = b/100 + b

⇒b′ = (b + 100b)/100 = 1.01 b

Clearly, the final perimeter > intitial Perimeter.

Now Perimeter = 2(1.01 l + 1.01 b)

∴ Percentage of change in Perimeter:-

[(2.02 l + 2.02 b) - (2l + 2b)]/[(2l + 2b)] × 100%

= (0.01) × 100%

= 1% (increase in perimeter).