Question

A triangular park has sides 120 m , 80 m , and 50 m . A gardener has to put fence all around it and also plant grass inside. How much area does he needs to plant

Answer 1

Given sides of triangular field = 120 m , 80 m , 50 m

Semi-perimeter of triangle (s) =  $\frac{a+b+c}{2}$

= $\frac{120 + 80 + 50}{2}$

=$\frac{250}{2}$

= 125 m

Using Heron's formula for area of triangle

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

=$\sqrt{125(125-120) (125-80) (125-50)}$

=$\sqrt{125 (5) (45) (75)}$

=$\sqrt{5*5*5*5*9*5*25*3}$

=5*5*5*3$\sqrt{15}$

= 625$\sqrt{15}$ m²

Therefore , area of grass to be planted in the field = 625$\sqrt{15}$ m²

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P.S.

You can take approx. value of $\sqrt{15}$ i.e. 3.87 but i recommend it to keep it n that form only for simplicity.

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I hope you understand.