Question

The ratio of the length of sides of a triangular park is 2:3:4 ,perimeter of the park is 216m ,find the area of the park and find the length of sides of a triangular park​

Answer 1

Step-by-step explanation:

Let the common factor be "x"

so,

we will let length of sides of park as " 2x, 3x and 4x".

SINCE,

PERIMETER OF A TRIANGLE = SUM OF ALL SIDES

THEREFORE,

2x+3x+4x = 216 m

= 9x = 216 m

= x = 24 m

SIDES OF TRIANGLE ARE :-

2x = 2×24 = 48

3x = 3×24 = 72

4x = 4×24 = 96

Semiperimeter = 216/2 = 108 m

AREA OF TRIANGLE = √(108(108-48)(108-72)(108-96)

= √(108(60)(36)(12)

= 5458.88 m² ( ANS )

WE HAVE FOUND AREA USING Herons formula

Answer 2

Required Answer :

$\underline{ \boxed{ \sf \pmb{Length \: of \: the \: sides \: of \: the \: park \: is \: 48 \: m, \: 72 \: m \: and \: 96 \: m}}} \red \bigstar$

$\underline{ \boxed{ \sf \pmb{Area \: of \: the \: park = 1673.13 \: {m}^{2} }}} \red \bigstar$

Given :

• Ratio of the length of the sides of a triangular park = 2 : 3 : 4
• Perimeter of the park = 216 m

To find :

• Length of the sides of the park
• Area of the park

Solution :

Let us assume that :

⇒ First side of the park = 2x

⇒ Second side of the park = 3x

⇒ Third side of the park = 4x

Using formula,

• Perimeter of triangle = a + b + c

where,

• a, b and c denotes the three sides of the triangle

Substituting the given values :

⇒ 2x + 3x + 4x = 216

⇒ 9x = 216

⇒ x = 216/9

⇒ x = 24

Substituting the value of x in the sides of the triangular park :

⇒ First side = 2x

⇒ First side = 2(24)

⇒ First side = 48 m

⇒ Second side = 3x

⇒ Second side = 3(24)

⇒ Second side = 72 m

⇒ Third side = 4x

⇒ Third side = 4(24)

⇒ Third side = 96 m

Therefore, the three sides of the triangular park = 48 m, 72 m and 96 m.

Area of the park :

Using formula,

• Semi perimeter = Perimeter ÷ 2

Substituting the given values :

⇒ Semi perimeter = 216 ÷ 2

⇒ Semi perimeter = 108 m

Using formula,

• Heron's formula = √s(s - a)(s - b)(s - c)

Substituting the given values :

⇒ Area = √108(108 - 48)(108 - 72)(108 - 96)

⇒ Area = √108(60)(36)(12)

⇒ Area = 1673.13

Therefore, the area of the triangular park = 1673.13 m²