Question

The sides of a triangulae field are in the
ratio of 4:5:6 Then find the area of
the field if its perimeter
is
300 m.​

Answer 1

let the sides be 4x,5x,6.

therefore

perimeter=sum of sides

300=4x+5x+6x

300=15x

x=300/15

x=20

the sides are :4x=4×20=80

5x=5×20=100

6x=6×20=120

now let's find out the area.

by heron's formula

area=root s(s-a)(s-b)(s-c). (here s means semiperimeter)

so the semiperimeter is the total perimeter/2

which is 300/2

so the semiperimeter is 150

now we can apply heron's formula

root of 150(150-80)(150-100)(150-120)

root of 150(70)(50)(30)

so we get the area as

3968.626

Answer 2

Correct Question :

The sides of a triangular field are in the ratio of 4:5:6, then find the area of the field if its perimeter is 300 m.

Given :

• The sides of a triangular field are in the ratio of 4:5:6.
• Perimeter of the triangular field = 300m.

To Find :

• The area of the field.

Solution :

According to the question :

Let, the sides of the field are 4x, 5x and 6x .

Using Formula : Perimeter of triangle = Sum of all sides

⟶ 300 = 4x + 5x + 6x

⟶ 300 = 15x

⟶ x = 300/15

⟶ x = 20

Hence, the sides will be :

• 4x = 4(20) = 80m
• 5x = 5(20) = 100m
• 6x = 6(20) = 120m

For Finding area of the given triangle, we should have to use Heron's Formula as all the sides of the triangle are different.

Using Formula : $\underline{ \boxed{ \sf{ \sqrt{s(s - a)(s - b)(s - c)} }}}$

Let, (a = 80), (b = 100), (c = 120)

• Finding s,

$\longrightarrow$ $\sf{ s = \dfrac{a + b + c}{2} }$

$\longrightarrow$ $\sf{s = \dfrac{ 80 + 100 + 120}{2} }$

$\longrightarrow$ $\sf{s =\cancel{ \dfrac{ 300}{2} }}$

$\longrightarrow$ $\sf{s = 150}$

• Hence we got s = 150

Putting the values in the Formula $\bf{ \sqrt{s(s - a)(s - b)(s - c)} }$

$\longrightarrow \sf{\sqrt{150(150 - 80)(150 - 100)(150 - 120)} }$

$\longrightarrow \sf{\sqrt{150 \times 70 \times 50 \times 30)} }$

$\longrightarrow \sf{\sqrt{15,750,000}}$

$\longrightarrow \sf{3,968.62}$m²

• Hence, the area of the triangle field = 3,968.62 m²