Question

The perimeter of a triangular garden is 300cm and its sides are in the ratio 3:5:4 .Using Herons formula find the area of the triangular garden
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Answer 1

Answer:

GIVEN :

The perimeter of a triangular garden is 300cm and its sides are in the ratio 3:5:4 .

TO FIND :

Using Herons formula find the area of the triangular garden

SOLUTION :

• Let sides be 3x ,5x & 4x

We know that : Perimeter of triangle = Sum of all sides

• =)300 cm =3x+4x+5x
• =) 300 cm = 12x
• =)25 cm = X

Sides of triangle = 75 cm ,100cm , 125 cm

Area is in above attachment

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@PHENOM

Answer 2

Answer:

• Perimeter of a triangular garden = 300 cm
• Sides of the triangle are on the ratio = 3:5:4
• Area of the triangle = ?

$\displaystyle\underline{\bigstar\:\textsf{According to the given Question :}}$

• So here we would first find the sides of the triangle using the ratios and perimeter that's given in the Question directly
• Then on substituting the values in the Heron's Formula would give us our Answer
• Herons Formula = √{s(s-a)(s-b)(s-c)}
• Sides = 3x,4x & 5x

$\displaystyle\sf :\implies Perimeter = Sum \ of \ all \ sides$

$\displaystyle\sf :\implies 900 = 3x+4x+5x$

$\displaystyle\sf :\implies 900 = 12x$

$\displaystyle\sf :\implies \dfrac{900}{12} = x$

$\displaystyle\sf :\implies \underline{\boxed{\sf x = 75}}$

So then the sides will be

➝ $\displaystyle\sf 3x = 3\times 75 = \textsf{ \textbf{225 cm}}$

➝ $\displaystyle\sf 4x = 4\times 75 = \textsf{ \textbf{300 cm}}$

➝ $\displaystyle\sf 5x = 5\times 75 = \textsf{ \textbf{375 cm}}$

$\displaystyle\underline{\bigstar\:\textsf{Area of the traingle :}}$

• Before finding the area of the triangle we have to find the semi perimeter (s) which is simply Perimeter/2
• Semi Perimeter = 900/2 = 450 cm

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

$\displaystyle\sf \dashrightarrow Area_{\triangle} = \sqrt{450(450-225)(450-300)(450-375)}$

$\displaystyle\sf \dashrightarrow Area_{\triangle} = \sqrt{450\times 225\times150\times 75}$

$\displaystyle\sf \dashrightarrow Area_{\triangle} = \sqrt{1139062500}$

$\displaystyle\sf \dashrightarrow \underline{\boxed{\sf Area_{\triangle} = 33750 \ cm^2}}$

$\displaystyle\therefore\:\underline{\textsf{ Area of the triangular garden is \textbf{33750 cm}}\sf {}^2}$