Chapter 12.7, Problem 54E

a.

To determine

To find: The partial derivative of $A_a,A_b\text{and}{A}_c$ if $A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$.

b.

To determine

To estimate: The change in area $A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$ when $a$ increase from $2.00\text{to}2.03$, $b$ decrease from $4.00\text{to}3.92$ and $c$ increase from $5.00\text{to}5.6$.

c.

To determine

To estimate: The percentage change in the area of an equilateral triangle

$A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$ if the length of all the sides increases by $p\%$.