Question

The sides of a triangular park are in the ratio 4:8:12. The perimeter is 600 m. Find its area.
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Answer 1

Step-by-step explanation:

let the sides be 4x , 8x, 12x. then write according to question and add 4x+8x+12x = 600. then write 24x = 600 and x= 25 then find the length of sides by putting the value of x

Answer 2

Given:-

• The sides of a triangular park are in the ratio 4:8:12.
• Perimeter is 600 m.

To find:-

• The area of a triangular park.

Solution:

• Let the sides be a = 4x, b = 8x and c = 12x.

As we know that,

• P = a + b + c units

Applying the values,

⇒ 600 = 4x + 8x + 12x

⇒ 600 = 24x

⇒ x = 600/24

⇒ x = 25

• Thus, the value of x is 25.

So,

• a = 4x = 4 × 25 = 100 m.
• b = 8x = 8 25 = 200 m
• c = 12x = 12 25 = 300 m.

Now,finding the semi-perimeter,

Formula required:-

• 2s = a + b + c

Applying the vales,

⇒ 2s = 100 + 200 + 300

⇒ 2s = 600

⇒ s = 600/2

⇒ s = 300 m

Next,Finding the area of the triangle.

Formula required:

• Area of triangle = √s(s-a)(s-b)(s-c) units.

Where,

• s = 300 m
• s - a = 300 - 100 = 200
• s - b = 300 - 200 = 100
• s - c = 300 - 300 = 0

Substituting the values,

$\\ :\implies\sf{Area\; of\; \triangle^{le}= \sqrt{300 \times (200) \times (100) \times (0)} } \\ \\ :\implies\sf{Area\; of\; \triangle^{le}= \sqrt{2 \times 2 \times5 \times 5 \times 3 \times 2 \times 2 \times 2 \times 5 \times 5 \times 2 \times 2 \times 5 \times 5 \times 0}}\\ \\ :\implies\sf{Area\; of\; \triangle^{le}=\sqrt{2^2 \times 5^2 \times 3 \times 2^2 \times 2 \times 5^2 \times 2^2\times 5^2 \times 0}}$

$\\ :\implies\sf{Area\;of\;\triangle^{le} = 2 \times 5 \times 2 \times 5 \times2\times 5 \sqrt{3 \times 2 \times 0}} \\ \\ :\implies\sf{Area\;\;of\;\triangle^{le}= 125 \times 8\sqrt{0}}\\ \\ :\implies\sf{Area\;\;of\;\triangle^{le}= 1000\;m^2}$

• ∴ Hence,the area is 1000 m².

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Formula's used here:-

• P = a + b + c units
• 2s = a + b + c units

• Area of triangle = √s(s-a)(s-b)(s-c) units.

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