Question

the side of a triangle plot are in the ratio of 3:5:7 and it's perimeter is 300m find its area ​

Answer 1

Answer:

Let the sides of a triangular plot is 3x , 5x and 7x

3x + 5x + 7x = 300 m

15x = 300

x = 300/15

x = 20

then the sides of triangular plot is

3x = (3 × 20) = 60

5x = (5 × 20) = 100

7x = (7 × 20) =140

now the area of triangular plot is

area =area =

\sqrt{s(s - a)(s - b)(s - c)}  

\sqrt{150(150 - 60)(150 - 100)(150 - 140)}  

1500 \sqrt{3 \:  \:  \:  {m}^{2} }

Step-by-step explanation:

Answer 2

Given :-

• Perimeter of triangle = 300m

• Sides of a triangle are in the ratio of 3 : 5 : 7

To find :-

• The area of triangle = ?

Solution :-

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

Perimeter of triangle = 300

⤇ a + b + c = 300

⤇ 3x + 5x + 7x = 300

⤇ 15x = 300

⤇ x = $\rm\cancel\dfrac{300}{15}$

⤇ x= 20

Now, we have

• First side of triangle (a) = 3x = 3 × 20 = 60m

• Second side of triangle (b) = 5x = 5 × 20 = 100m

• Third side of triangle (c) = 7x = 7 × 20 = 140m

Then,

$\rm\:s=\dfrac{a+b+c}{2}$

$\rm\longrightarrow\:s=\dfrac{60+100+140}{2}$

$\rm\longrightarrow\:s=\cancel\dfrac{300}{2}$

$\rm\longrightarrow\:s=150\:m$

Now,

By using Heron's formula,

$\rm\:Area\:of\:triangle=\sqrt{s(s-a)(s-b)(s-c)}$

$\rm\:Area\:of\:triangle=\sqrt{150(150-60)(150-100)(150-140)}$

$\rm\:Area\:of\:triangle=\sqrt{150\times\:90\times\:50\times\:10}$

$\rm\:Area\:of\:triangle=2\times{3}\times{5}\times{5}\times{5}\times{2}\sqrt{3}$

$\rm\:Area\:of\:triangle=1500\sqrt{3}\:{m}^{2}$

Hence,the area of triangle will be 1500√3 m².