Question

the area of a field in the shape of a triangle with each x meters is equal to the area of another triangulathe area of a field in the shape of a triangle with each x meters is equal to the area of another triangular field having sides 50m, 70m, and 80m. the value of x closed to

Answer 1

Answer:

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Answer 2

The value of x is closed to 63.25 m.

Explanation:

Heron's formula :

Area of triangle with sides a, b ,c =$\sqrt{s(s-a)(s-b)(s-c)}$ , where s is the semi-perimeter.

If sides of a triangle are 50m, 70m, and 80m , then $s=\dfrac{50+70+80}{2}=\dfrac{200}{2}=100$

By Heron's formula ,

Area of triangle = $\sqrt{100(100-50)(100-70)(100-80)}$

Area of triangle = $\sqrt{100(50)(30)(20)}$

Area of triangle = $\sqrt{3000000}=1000\sqrt{3}$

If all the sides of a triangle area equal ,then it is known as equilateral triangle .

Area of equilateral triangle =$\dfrac{\sqrt{3}(side)^2}{4}$

Area of equilateral triangle with side x=$\dfrac{\sqrt{3}(x)^2}{4}$

Since it is given that ,

Area of equilateral triangle with side x=Area of triangle with sides 50m, 70m, and 80m

$\Rightarrow \dfrac{\sqrt{3}(x)^2}{4}=1000\sqrt{3}$

$\Rightarrow x^2=1000\times4=4000\\\\\Rightarrow\ x=\sqrt{4000}$

$\approx63.25\ m$

Hence, the value of x is closed to 63.25 m.

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