Question

The Perimeter of a triangular field is 120 m and the sides are in the ratio of 25::15::20. Find its area??

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Answer 1

Answer:

area=600cm2

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Explanation:

perimeter=120

a+b+c=120

a=25x

b=15x

c=20x

25x+15x+20x=120

60x=120

x=2

a= 25x=50cm

b=15x=30cm

c=20x=40cm

using heron's formula

√s(s-a)(s-b)(s-c)

s=a+b+c/2

s=60

area= √60(60-50)(60-30)(60-40)

area= √60×10×30×20

area=√360000

area=600

Answer 2

Answer:

The perimeter of a triangular field is 120 m and the sides are in the ratio of 25::15::20. find its area

The perimeter of a triangular field =120m

Let the side =25x,15x,20x

Perimeter of a triangle =Sum of three side

$25x + 15x + 20x = 120$

$60x = \begin{gathered} \longmapsto \rm { \cancel{\dfrac{120}{60}} = x = 2}\\ \end{gathered}$

1st side (a)=25×2=50m

2nd side(b)=15×2=30m

3rd side (c)=20×2=40

Semi--perimeter(S)=

$\begin{gathered} \longmapsto \rm { {\dfrac{a + b + c}{2}} }\\ \end{gathered}$

$\begin{gathered} \longmapsto \rm { \cancel{\dfrac{120}{60}} = 60m}\\ \end{gathered}$

[By Heron's Formula]

$★Area(Δ)=s(s−a)(s−b)(s−c)$

$★Area(Δ)=s(s−50)(s−30)(s−40)$

$\sqrt{60(60 - 50)(60 - 30)(60 - 40)}$

$\sqrt{60 \times 10 \times 30 \times 20}$

$= 360000$

$★Area \: \: of \: \: (Δ) = 600m {}^{2}$