Question

a triangle has sides 17, 25 and 26 m find its area

Answer 1

$\textbf{\huge{ANSWER:}}$

Given:

Sides = 17 m , 25 m, 26 m

Area of a triangle can be also taken out by the Heron's Formula. That is:

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

Where,

s = Semi-perimeter ( Perimeter/2 )

a , b , c = Sides of the triangle

Putting the values in the formula:

s = Perimeter/2

Perimeter = 17 + 25 + 26 = 68

s = 68/2 = 34 m

ATQ:

$\sqrt{34(34 - 17)(34 - 25)(34 - 26)} \\ \\ = > \sqrt{34(17)(9)(8)} \\ \\ = > 204 \: {m}^{2}$

Hope it Helps!! :)

Answer 2

$\huge{\mathcal{Hi\: there!}}$

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Solution :

Let the sides of the triangle be

a = 17 m

b = 25 m

c = 26 m.

Now,

We will use Heron's Formula here, to find area of triangle.

According to which;

$\mathsf{Area \: of \: Δ = \sqrt{s(s - a)(s - b)(s - c)} }$

Here,

S stands for 'semi - perimeter'.

$\mathsf{s = \frac{a + b + c}{2} } \\ \\ \mathsf{s = \frac{17 + 25 + 26}{2} } \\ \\ \mathsf{s = \frac{68}{2} } \\ \\ \mathsf{s = 34 \: m}$

Now,

$\mathsf{area \:of \: Δ } = \\ \\ \mathsf{ \sqrt{34(34 - 17)(34 - 25)(34 - 26)} } \\ \\ \mathsf{34 \times 17 \times 9 \times 8} \\ \\ \mathsf{ \sqrt{41616} } \\ \\ = \mathsf{204 \: m {}^{2} }$

Hence, the area of triangle is 204 m²

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Thanks for the question !

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