AP EAMCET Engineering 22 Sep 2020 Shift 2 Paper

Let side of square =x
Given, percentage change in side =6%
‌

dx

x

×100=6%....(i)
We have, A=x2
Differentiate w.r.to ' x '
‌

dA

dx

=2x⇒dA=2xdx
Dividing by x2 on both sides
‌

dA

x2

=2⋅‌

xdx

x2

‌

dA

A

=2‌

dx

x

[∵A=x2]
Now, multiply by 100
‌

dA

A

×100=2×(‌

dx

x

×100)
Percentage change in Area =2×6% [from Eq. (i) ]
=12%