Question

What is the Golden Triangle in India? Find the area of it using Heron's formula in Sq km.​

Answer 1

Answer:

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Step-by-step explanation:

In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria,[1] gives the area of a triangle when the length of all three sides are known. Unlike other triangle area formulae, there is no need to calculate angles or other distances in the triangle first.

Answer 2

Answer:

Step-by-step explanation:

India's Golden Triangle comprises the three most visited cities in the country's north-west - Delhi, Agra and Jaipur, which are all connected to each other by good road and rail links. On the map, these form a roughly equilateral triangle, some 240km along each side.

Perimeter of the golden triangle,

$\[\begin{array}{l} = 3 \times 240\\ = 720\,km\end{array}\]$

Therefore,

$\[s = \frac{{720}}{2}\]$

$\[ \Rightarrow s = 360\]$

Use heron's formula to calculate the area,

$\[\begin{array}{l} = \sqrt {360\left( {360 - 240} \right)\left( {360 - 240} \right)\left( {360 - 240} \right)} \\ = \sqrt {360 \times 120 \times 120 \times 120} \\ = 120 \times 120\sqrt 3 \\ = 14400\sqrt 3 \;sqkm\end{array}\]$

Hence, the area of the golden triangle is $\[14400\sqrt 3 \]$ Sq km.