Question

Triangle RST has sides measuring 22 inches and 13 inches and a perimeter of 50 inches. What is the area of triangle RST? Round to the nearest square inch. (using heron's formula)

Answer 1

$\bf \textit{Heron's Area Formula}\\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} a=22\\ b=13\\ c=\stackrel{perimeter}{50}-22-13\\ \qquad 15\\ s=\frac{a+b+c}{2}\\ \qquad 25 \end{cases} \\\\\\ A=\sqrt{25(25-22)(25-13)(25-15)}\implies A=\sqrt{25(3)(12)(10)} \\\\\\ A=\sqrt{25(360)}\implies A=\sqrt{9000}\implies A\approx 94.868329805$

Answer 2

Answer:

95 square inches

Step-by-step explanation: