Question

the sides of a triangular plot are in the ratio of 3:5:7 and it's semi perimeter is 150m. find its area?​

Answer 1

Given :

• Ratio of sides of the triangle = 3 : 5 : 7

• Semi-Perimeter of the triangle = 150 m.

To find :

The area of the triangle.

Solution :

Let the sides of the triangle be 3x , 5x and 7x.

We know the formula for Semi-perimeter of a triangle .i.e,

Semi perimeter = (a + b + c) × ½

By using it and substituting the values in it, we get :

==> 150 = (3x + 5x + 7x) × ½

==> 150 = 15x × ½

==> 150 × 2 = 15x

==> 300 = 15x

==> 300/15 = x

==> 20 = x

∴ x = 20 m.

Hence the value of x is 20 m.

Now let's find the sides of the triangle :

• First side = 3x

==> a = 3 × 20

==> a = 60 m.

∴ a = 60 m.

Hence the first side of the triangle is 60 m.

• Second side = 5x

==> b = 5 × 20

==> b = 100

∴ b = 100 m.

Hence the second side of the triangle is 100 m.

• Third side of the triangle = 7 x

==> c = 7 × 20

==> c = 140

∴ c = 140 m.

Hence the third side of the triangle is 140 m.

To find the area of the triangle :

We know the heron's Formula.i.e,

⠀⠀⠀⠀⠀⠀⠀⠀A = √{(s - a)(s - b)(s - c)}

Where :

• A = Area
• s = Semi-perimeter
• a,b and c = Sides of the triangle

Now using the heron's formula and substituting the values in it,we get :

==> A = √{150 × (150 - 60) × (150 - 100) × (150 - 140)}

==> A = √{150 × 90 × 50 × 10}

==> A = √{3 × 5 × 10 × 3 × 10 × 5 × 10 × 10}

==> A = √{3² × 5² × 10² × 10²}

==> A = 3 × 5 × 10 × 10

==> A = 1500

∴ A = 1500 m².

Hence the area of the triangle is 1500 m².

Answer 2

Question

The sides of the triangular plot are in the ratio of 3 : 5 : 7. and it's semi perimeter is 150m . Find its area.

Given

• The sides of a triangular plot are in the ratio of 3 : 5 : 7
• It's semi perimeter is 150 m.

Required to Find

Area of the triangular plot.

The sides of a triangular plot are in the ratio 3 : 5 : 7. so

Let the sides of the triangle be 3x , 5x and 7x

It is given that the perimeter of the triangle is 300 meter so ,

3x + 5x + 7x = 300

15x = 300

x = 20

Therefore , the sides of the triangle are

60 , 100 and 140.

By using herons formula :

$\sf \: s = \dfrac{60 \: + \: 100 \: + \: 140}{2} = \dfrac{ \: 300 \: }{ \: 2 \: }$

Area of the triangle :

$\sf \: a = \sqrt{s(s - a)(s - b)(s - c)}$

$\sf \implies \sqrt{150(150 - 60)(150 - 100)(150 - 140)}$

$\sf \implies \sqrt{150 \times 90 \times 50 \times 10} = \sqrt{6750000}$

$\sf \implies \: 1500 \sqrt{3} {m}^{2}$

$\sf \: hence \: the \: area \: of \: the \: triangular \: plot \: is \: 1500 \sqrt{3} {m}^{2}$