Question

If $A$ is the area of a triangle in ${cm}^2$, whose sides are $9cm,10cm$ and $11cm$, then which one of the following is correct?

• A. $A<40{cm}^2$
• B. $40{cm}^2<A<45{cm}^2$
• C. $45{cm}^2<A<50{cm}^2$
• D. $A>50{cm}^2$

Answer 1

Answer: (B)

$40{cm}^2<A<45{cm}^2$

$S=\frac{a+b+c}{2}=\frac{9+10+11}{2}=15$

Using Heron's formula

$A=\sqrt{S(S-a)(S-b)(S-c)}$

$=\sqrt{15\times 6\times 5\times 4}=\sqrt{1800}=42-42$

$\Rightarrow 40<A<45$