Question

The perimeter of a triangle is 170 feet and the sides are in the ratio of 25:14:12. Find the area of the triangle.A. 496.08 ft²B. 153.45 ft²C. 494.35 ft²D. 107.24 ft²

Answer 1

The perimeter of a triangle is 170 feet

The sides are in the ratio of 25:14:12

The total ratio 25+14+12=51

Let's calculate each side

$\begin{gathered} \text{First side} \\ \frac{25}{51}\times170=\frac{250}{3}=83.33 \\ \\ \text{second side} \\ \frac{14}{51}\times170=\frac{140}{3}=46.67 \\ \\ \text{Third side} \\ \frac{12}{51}\times170\text{ =40} \end{gathered}$

The three sides are given, so we use the Hero formula to calculate the area of the triangle.

$\begin{gathered} \text{Area =}\sqrt[]{s(s-a)(s-b)(s-c)} \\ \\ S=\frac{a+b+c}{2} \end{gathered}$

a = 83.33ft, b=46.67ft and c=40ft

$\begin{gathered} S=\frac{83.33+46.67+40}{2} \\ \\ S=\frac{170}{2} \\ S=85 \\ \end{gathered}$

$\begin{gathered} \text{Area =}\sqrt[]{85(85-83.33)(85-46.67)(85-40)} \\ \\ \text{Area =}\sqrt[]{85(1.67)(38.33)(45)} \\ \\ \text{Area =}\sqrt[]{85(1.67)(38.33)(45)} \\ \\ \text{Area =}\sqrt[]{244842.4575} \\ \text{Area = 494.35 square ft} \end{gathered}$

The correct option is C