Question

two sides of triangular field are 85 M and 154 m in length and its perimeter is 324 M. find the area of field and the length of the perpendicular from the opposite vertex on the site measuring 154 m

Answer 1

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Answer 2

Answer:

We are given that two sides of triangular field are 85 M and 154 m

Perimeter of triangle = 324 M

Let the third side be x

Perimeter of triangle = Sum of all sides

                                  = 85+154+x

                                  = 239+x

Since we are given that Perimeter of triangle = 324 M

So, 324= 239+x

324-239 = x

85=x

Now we will use heron's formula to find the area of triangle

a = 85 m

b = 154 m

c = 85 m

$Area = \sqrt{s(s-a)(s-b)(s-c)}$

$s=\frac{a+b+c}{2}$

Substitute the values :

$s=\frac{85+154+85}{2}$

$s=162$

$Area = \sqrt{162(162-85)(162-154)(162-85)}$

$Area = 2772$

So, Area of triangle is 2772

Now to find the length of the perpendicular from the opposite vertex on the site measuring 154 m

Area = $\frac{1}{2} \times Base \times Height$

$2772=\frac{1}{2} \times 154 \times Height$

$\frac{2772 \times 2}{154} =Height$

$36=Height$

Hence  Area of triangle is 2772  and he length of the perpendicular from the opposite vertex on the site measuring 154 m is 36 m