Question

The sides of a triangular field are in the ratio of 5:6:7. If its perimeter is 3600m, find the area of that land

Answer 1

perimeter=a+b+c

let a=5x, b=6x &c=7x

3600=5x+6x+7x

3600=18x

X=3600/18

X=200

a=5x=5(200)=1000m

b=6(200)=1200m

c=7(200)=1400m

s=p/2=3600/2

s=1800m

a=√(s-a)(s-b)(s-c)

a=√(800)(600)(400)

a=1000×4√3=4000√3

Answer 2

The area of the triangular field is 240000√6 m².

Given:

• The sides of a triangular field are in the ratio of 5:6:7.
• If its perimeter is 3600m.

To find:

• Find the area of the land.

Solution:

Formula to be used:

• Apply heron's formula: $\bf Ar.(\triangle ABC) = \sqrt{s(s - a)(s - b)(s - c)}$ here,s: semiperimeter and a, b and c are sides of triangle.

Step 1:

Find the sides of the triangle.

ATQ,

The ratio of sides are 5:6:7, let k is the common factor of the ratio.

So,

$5k + 6k + 7k = 3600$

$18k = 3600$

$\bf k = 200$

Thus,

Sides of triangular field are 1000m, 1200 m and 1400 m.

Step 2:

Calculate the area of triangular field.

Here

$s = 1800$

$a = 1000 \\ b = 1200 \\ c = 1400$

$= \sqrt{1800(1800 - 1000)(1800 - 1200)(1800 - 1400)}$

$= \sqrt{1800 \times 800 \times 600 \times 400}$

$=\sqrt{18 \times 8 \times 6 \times 4 \times {10}^{8} }$

$= {10}^{4} \sqrt{(24)^2 \times 6 }$

Area of triangular field$\bf = 240000 \sqrt{6} \: {m}^{2}$

Thus,

The area of triangular field is 240000√6 m².

Learn more:

1) Find the area of the triangle whose lengths of sides are 15m, 17m, 21m (use Heron’s Formula) and verify your answer by u...

https://brainly.in/question/5484018

2) The perimeter of an isosceles triangle is 44cm and the ratio of the equal side to its base is 4:3. The area of the trian...

https://brainly.in/question/33628961

#SPJ3