Question

The sides triangler plots are in the ratio of 3:5:7 and its perimeter is 300 m find its area​

Answer 1

Answer:

212.132034356m²

Step-by-step explanation:

Let the sides be 3x , 5x , 7x respectively

So, 3x+5x+7x = 300

15x = 300

x = 300/15 = 20m

Hence the Sides of triangle are

60m , 100m , 140m

Semi perimeter = 300/2 = 150

Area of triangle by heron's formula

$= \sqrt{(150 - 60)(150 - 100)(150 - 140)} \\ = \sqrt{90 \times 50 \times 10} \\ = 212.132034356 {m}^{2}$

Answer 2

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

$\sf \: The \: sides \: of \: triangular \: plot \: are \: in \: the \: ratio \: of \: 3:5:7$

$\sf \: Perimeter \: of \: the \: Triangular \: plot \: is \: 300 \: meter$

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

$\sf \: We \: have \: to \: find \: it's \: all \: the \: actual \: Sides \: and \: it's\: area.$

$\star \: \bf\underline{ So, \: Let's \: Start} \: \star$

$\boxed{ \purple{\sf \: Perimeter \: of \: the \: \triangle \: = \: Sum \: of \: all \: Sides. \: }}$

$\sf \: Let \: the \: Sides \: of \: triangular \: plot \: be \: 3x, \: 5x, \: 7x.$

$\bf \: \underline{According \: to \: the \: Formula } \: :$

$\sf \: 3x \: + \: 5x \: + 7x \: = \: 300$

$\sf \: 15x \: = \: 300$

$\sf \: x \: = \: \dfrac{300}{15}$

$\sf \: x \: = \: 20$

$\sf \: So, \: Now \: the \: actual \: sides \: of \: the \: Triangular \: plot \: are \: :$

$\red{ \sf \: \bigstar \: First \: side : }$

$\sf \: 3x \: = \: 3 \: \times \: 20 = 60$

$\red{ \sf \: \bigstar \: Second\: side : }$

$\sf \: 5x \: = \: 5\: \times \: 20 = 100$

$\red{ \sf \: \bigstar \: Third\: side : }$

$\sf \: 7x \: = \: 7\: \times \: 20 = 140$

$\sf \: Hence \: the \: sides \: of \: Triangular \: plot \: are \: 60, \: 100, \: 140.$

$\underline{ \sf \: Now \: we \: will \: find \: the \: Area \: of \: that \: Triangular \: plot.}$

$\sf \: Semi-perimeter = \dfrac{a + b + c}{2}$

$\sf \: Putting \: the \: value \: into \: the \: formula \: :$

$\sf \: \longrightarrow \dfrac{60 + 100 + 140}{2}$

$\sf \: \longrightarrow \dfrac{300}{2}$

$\green{ \sf \: Semi-perimeter = 150}$

$\bf \: Now,$

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

$\sf \: Putting \: the \: value \: into \: the \: formula \: :$

$\sf \: A = \sqrt{150(150-60) \: (150-100) \: (150-140)}$

$\sf \: A = \sqrt{150 \: \times \: 90\: \times \: 50 \times \: 10 }$

$\sf \: A = \sqrt{6750,000 }$

$\sf \: A = 1500\sqrt{3 }$

$\purple{ \sf \: A = 1500\sqrt{3 } \: \: m^{2} }$