Chapter 14.2, Problem 39E

To determine

To find: The pairs of numbers in which the area of $\Delta ABC$ lies.

Answer to Problem 39E

The correct option is A.

Explanation of Solution

Given:

The given figure is as:

  

Calculation:

The perimeter of triangle is calculated as:

  $p=7+10+5$

The area of triangle is calculated as:

  $\begin{array}{c}\text{Area}=\sqrt{\frac{p}{2}\left(\frac{p}{2}-a\right)\left(\frac{p}{2}-b\right)\left(\frac{p}{2}-c\right)}\\ =\sqrt{11\left(11-7\right)\left(11-5\right)\left(11-10\right)}\\ =16.25\end{array}$

The area is $16.25$ square units.

Therefore the correct option is A.