Question

Find the area of triangular field whose sides are 50m, 45m and 35m

Answer 1

Hello!

Find the area of rectangular Field in acres whose sides are 50 m, 45 m and 35 m.

We have the following data:

$a = 50\:m$

$b = 45\:m$

$c = 35\:m$

$Area = ?\:(in\:m^2)$

Note: As we know the three sides of the triangle, let's apply Heron's formula to find the area.

• [First Step] Let's find the semiperimeter of the triangle, let's see:

$S = \dfrac{a+b+c}{2}$

$S = \dfrac{50+45+35}{2}$

$S = \dfrac{130}{2}$

$\boxed{S = 65\:m}\Longleftarrow(semiperimeter)$

• [Second Step]  Let's find the area of ​​the triangle, let's see:

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

$Area = \sqrt{65*(65-50)*(65-45)*(65-35)}$

$Area = \sqrt{65*(15)*(20)*(30)}$

$Area = \sqrt{65*(9000)}$

$Area = \sqrt{585000}$

Let's factor for the least common multiple

585000 | 5

117000 | 5

23400 | 5

4680 | 5

936 | 3

312 | 3

104 | 2

52 | 2

26 | 2

13 | 13

1 \___ = $5^4 * 2^3 * 3^2 * 13 = \boxed{5^2*5^2*2^2*2*3^2*13}$

then:

$Area = \sqrt{585000}$

$Area = \sqrt{ 5^2*5^2*2^2*2*3^2*13}$

$Area = 5*5*2*3\sqrt{2*13}$

$\boxed{\boxed{Area = 150\sqrt{26}\:m^2\:\:\:or\:\:\:Area \approx 764.85\:m^2}}\:\:\:\:\:\:\bf\blue{\checkmark}\bf\green{\checkmark}\bf\red{\checkmark}$

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Answer 2

anwer in image .

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