Question

 A triangle shaped land has the sides in the ratio 3:5:7, if its perimeter is 300 meter. What will be the area of the land ? एक त्रिभुज के आकार के भू-खंड का अनुपात 3: 5: 7 है। इसकी परिमाप 300 मीटर है। इस भूमि का क्षेत्रफल क्या होगा? *​

Answer 1

HELLO DEAR,

GIVEN:-

sides of triangle are in ratio of 3 : 5 : 7.

perimeter of triangle is p = 300m

NOW,

let the sides of triangle be 3x , 5x , 7x.

therefore,

p = 3x + 5x + 7x

=> 300 = 8x + 7x

=> 300 = 15x

=> x = 20m.

hence, side of triangle be 3x , 5x , 7x

or 60 , 100 , 140 respectively.

since, area of triangle = [tex]\sf{\sqrt{s(s - a)*(s - b)*(s - c)}}[/tex]

where a , b , c are the sides of triangle and s is the semiperimeter of triangle.

s = p/2 = 150m

$\sf{ \rightarrow A = \sqrt{150(150 - 60)(150 - 100)(150 - 140)}}$

$\sf{\rightarrow A = \sqrt{150*90*50*10}}$

$\sf{\rightarrow A = 100\sqrt{15*15*3}}$

$\sf{\rightarrow A = 1500\sqrt{3}meters}$

I HOPE IT'S HELP YOU DEAR,

THANKS

Answer 2

Given :-

• Side ratio of Triangle shaped land = 3 : 5 : 7 .
• Perimeter of land = 300m .

To Find :-

• Total area of land ?

Solution :-

Let us assume that, sides of Triangle shaped land are 3x, 5x and 7x respectively.

Than,

→ Perimeter of land = sum of all sides.

→ 3x + 5x + 7x = 300

→ 15x = 300

→ x = 20.

Therefore,

→ First side = 3x = 3*20 = 60m.

→ second side = 5x = 5*20 = 100m.

→ Third side = 7x = 7*20 = 140m.

Now,

→ By Heron's formula area of ∆ with three sides as a,b and c and semi - perimeter as s is :-

• √{s(s-a)(s-b)(s-c)}

So,

→ semi-perimeter of land = (Perimeter/2) = (300/2) = 150m.

Putting all values now in Heron's formula we get :-

→ Area = √{150 * (150-60) * (150 - 100) * (150 - 140)}

→ Area = √{150 * 90 * 50 * 10}

→ Area = √{3 * 50 * 3 * 30 * 50 * 10}

→ Area = √{(3)² * (50)² * 3*(10)²}

→ Area = 3 * 50 * 10 * √3

→ Area = 1500√3 m².

Hence, Area of Land is 1500√3m².