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The sides of a triangular field are in the ratio of 5:6: 7. If its perimeter is 3600 m, find the area of that land.​

1 Answer

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Answer:

587877.5383m^2

Explanation:

First off, we need to find the 3 sides of the triangle. To do this, we need to know that all the sides add up to 3600m. So 5 + 6 + 7 = 3600m. Since we don't know what 5, 6 and 7 are, we have to find out what is 1 worth. So adding them all up equals to 18, so 18 = 3600m. To find 1, simply divide 3600m by 18 which = 200m. Now to find all the sides, multiply each side by 200.

5*200 = 1000m

6*200 = 1200m

7*200 = 1400m

Then to find the area, we will need to use the formula 1/2abSinC.

However to do this, we need an angle. So to find that angle we will use the cosine rule A = cos-1(b^2 + c^2 -a^2/2bc). This will lead to A = 44.4153086º.

Then we can use the area formula to find the area of the land. This will give an area of 587877.5383m which you can round up to whichever extent you want. I have attached a photo with the working out for everything.

The sides of a triangular field are in the ratio of 5:6: 7. If its perimeter is 3600 m-example-1
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