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} \\ (25)/(51)*170=(250)/(3)=83.33 \\ \\ \text{second side} \\ (14)/(51)*170=(140)/(3)=46.67 \\ \\ \text{Third side} \\ (12)/(51)*170\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=(a+b+c)/(2) \end{gathered}`

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

`\begin{gathered} S=(83.33+46.67+40)/(2) \\ \\ S=(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