Answer:
257.2 square inches
Explanation:
Given the three sides of a triangle, the area is found using Heron's formula:
[tex]\begin{gathered} \text{Area}=\sqrt[]{s(s-p)(s-q)(s-r)} \\ \text{Where p,q,r are the side lengths} \\ s=\frac{p+q+r}{2} \end{gathered}[/tex]
First, find the value of s:
[tex]s=\frac{14+37+38}{2}=\frac{89}{2}=44.5\text{ inches}[/tex]
Next, substitute the values into the formula:
[tex]\begin{gathered} \text{Area}=\sqrt[]{s(s-p)(s-q)(s-r)} \\ =\sqrt[]{44.5(44.5-14)(44.5-37)(44.5-38)} \end{gathered}[/tex]
Finally, simplify:
[tex]\begin{gathered} =\sqrt[]{44.5(30.5)(7.5)(6.5)} \\ =\sqrt[]{66165.9375} \\ =257.23 \\ \approx257.2\text{ square inches} \end{gathered}[/tex]
The area of triangle PQR is 257.2 square inches (to the nearest 10th of a square inch).
