Question

The perimeter of a triangle is 300 m. If its sides are in the ratio 3 : 5 : 7. Find the area of the triangle.

Answer 1

Whenever we are given the measurement of all sides of a triangle, we basically look for Heron’s formula to find out the area of the triangle. If we denote area of the triangle by A, then the area of a triangle having sides a, b, c and s as semi-perimeter is given by;

Where,

We are given, and

Here,

Using these data we will find the sides of the triangle. Suppose the sides of the triangle are as follows,

Since, so

Now we know each side that is,

Now we know all the sides. So we can use Heron’s formula.

The area of the triangle is;

$$\begin{gathered} \mathrm{A}=\sqrt{\mathrm{s}\left(\mathrm{s}-\mathrm{a}\right)\left(\mathrm{s}-\mathrm{b}\right)\left(\mathrm{s}-\mathrm{c}\right)} \\ =\sqrt{150\left(150-60\right)\left(150-100\right)\left(150-140\right)} \\ =\sqrt{150\left(90\right)\left(50\right)\left(10\right)} \\ =100\sqrt{15\times 9\times 5} \\ =100\sqrt{5\times 3\times 3\times 3\times 5} \\ =100\times 3\times 5\sqrt{3} \\ =\boxed{1500\sqrt{3}{\mathrm{m}}^2} \end{gathered}$$