Question

The side of triangle plot are in the ratio of 6:7:8 and perimeter is 420 m find area

Answer 1

Hope it may be helpful to you..

Answer 2

Concept:

Triangles are three-sided polygons, sometimes called trigon (although less commonly). Every triangle has three sides and three angles, some of which can be equal.

Given:

we are given that the side of triangle in the ratio of $6:7:8$ and their perimeter is $420m$.

To find:

We have to find the area of triangle.

Solution:

Let sides of a triangular field be

$a=6x,b=7x$ and$c=8x$.

The perimeter of a triangular field, $2s=a+b+c$

$\begin{aligned}420&=6x+7x+8x\\420&=21x\\\frac{420}{21}&=x\\20m&=x\end$

Sides of a triangular field are

$\begin{aligned}a&=6\times 20\\ &=120\\b&=7\times 20\\&=140\end{aligned}$

And

$c=8\times 20\\c=160m$

Now, semi-perimeters $s$ is given by

$\begin{aligned}s&=\frac{a+b+c}{2}\\ &=\frac{120+140+160}{2}\\ &=\frac{420}{2}\\ &=120\end$

Using the Heron's formula to find the Area.

Area of the triangular field $=\sqrt{s(s-a)(s-b)(s-c)}$ [by Heron’s formula].

$\begin{aligned}A&=\sqrt{210(210-120)(210-140)(210-160)}\\ &=\sqrt{210\times 90\times 70\times 50}\\ &=100\sqrt{21\times 9\times 7\times 5}\\ &=100\sqrt{7\times 3 \times 3^2 \times 7\times 5 }\\ &=100\times 3 7\times \times \sqrt{15}\\ &=2100\sqrt{15}m^2\end$

Hence, the area of the triangular field is $2100\sqrt{15}m^2$.

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