Question

The sides of a triangular field are 15 m, 20 m and 25 m. Find the area of

the triangle.​

Answer 1

$\bf \underline{ \underline{\maltese\:Given} }$

$\sf Sides \: of \: triangular \: field \: are \: 15 \: m, \: 20 \: m \: and \: 25 \: m.$

$\bf \underline{ \underline{\maltese\:To \: find } }$

$\sf \implies Area \: of \: triangular \: field = \: ?$

$\bf \underline{ \underline{\maltese\:Solution } }$

$\sf Using \: Heron's \: formula :$

$\underline{\boxed{\sf{Area_{\triangle} = \sqrt{s(s - a)(s - b)(s - c)}}}}$

$\bf \underline{ Now},$

$\sf \implies s \: = \: \dfrac{a + b + c}{2}$

$\sf \implies s \: = \: \dfrac{15 + 20 + 25}{2}$

$\sf \implies s \: = \: \cancel{\dfrac{60}{2}}$

$\sf \implies s \: = \: 30$

$\underline{ \sf \: Thus, \: semi-perimeter = 30\:m }$

$\bf \underline{Now}, \sf \: area \: of \: triangle :$

$\sf{Area_{\triangle} = \sqrt{s(s - a)(s - b)(s - c)}}$

$\sf{Area = \sqrt{30(30 - 15)(30 - 20)(30- 25)}}$

$\sf{Area = \sqrt{30 \times 15 \times 10 \times 5}}$

$\sf{Area = \sqrt{2 \times 3 \times 5 \times 3 \times 5 \times 2 \times 5 \times 5}}$

$\sf{Area = 2 \times 3 \times 5 \times 5 }$

$\sf{Area = 150 \: m} ^{2}$

$\underline{ \boxed{ \red{\bf \: Thus , \: area \: of \: triangle\: is\: 150 \: m^2} }}$

Answer 2

Answer:

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