Question

The sides of a triangular plot are in the ratio of 3:5:7 and its perimeter is 300 m. Its area is:

• A. $1500\sqrt{2}{m}^2$
• B. $1500\sqrt{3}{m}^2$
• C. $1425\sqrt{2}{m}^2$
• D. $1500m^2$

Answer 1

The correct option is B

$1500\sqrt{3}{m}^2$

Suppose that the sides, in metres, are 3x, 5x and 7x.
Then, we know that 3x + 5x + 7x = 300.(perimeter of the triangle)
Therefore, 15x = 300,

$\Rightarrow$ x = 20.
So the sides of the triangle are $3\times 20m,5\times 20m$ and $7\times 20m$
i.e., 60 m, 100 m and 140 m

We have $s=\frac{60+100+140}{2}m=150m$
Area of the triangle
$=\sqrt{150(150-60)(150-100)(150-140)}{m}^2$
$=\sqrt{150\times 90\times 50\times 10}{m}^2$

$=1500\sqrt{3}{m}^2$.