Respuesta :

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).

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