Question

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

Answer 1

Let the side be 3x ,5x,7x
Perimeter of the Triangle=sum of all sides
3x+5x+7x=300
15x=300
x=300/15
x=20
3x=60,5x=100,7x=140
If we take base 3x and height 5x
then the area will be
area of the Triangle =1/2×base×height
1/2×60×100
300

Answer 2

HELLO FRIEND HERE IS YOUR ANSWER,,,,,,,,

To find the area of the triangle, we've to consider the sides of the triangle as the variables of the following sides "3a" , "5b" and "7b" which is equalling to its perimeter that is "300m"

Therefore, 3a + 5b + 7b = 300 meters

$\bf{= 8a + 7a = 300 \: m}$

$\bf{= 15a = 300 \: m}$

$\bf{a = \frac{300}{15}}$

$\bf{a = 20 \: meters}$

Therefore, by substituting the value of a = 20 meters into the variables of triangle sides , we get ,,,

$= > \: \: 3 \times 20 \: m \\ \\ \\ = > 60 \: m \\ \\ \\ = > \: \: 5 \times 20 \: m \\ \\ \\ = > 100 \: m \\ \\ \\ = > \: \: 7 \times 20 \: m \\ \\ \\ = > 140 \: m$

All three sides have 60, 100 and 140 meters respectively according to their positions of sides in a triangle.

Perimeter of the triangle is = 300 meters

Therefore semi-perimeter of the triangle is =

$\bf{= \frac{300}{2} \: m}$

$\bf{= 150 \: m}$

By applying the principles and rules of Heron's formula which states the given three sides.

$\boxed{\bf{Area = \sqrt{s \: (s - a) \: (s - b) \: (s - c)}}}$

Therefore, substitute the given sides , a = 60 m, b = 100 m, c = 140 m and semi-perimeter "s" = 150 m.

$\bf{Area = \sqrt{150 \: (150 - 60) \: (150 - 100) \: (150 - 140)}}$

$\bf{Area = \sqrt{150 \times 90 \times 50 \times 10}}$

Split the values to cancel out the given value of "30" and "50" into 10 times of 5.

$\bf{Area = \sqrt{30 \times 5 \: 30 \times 3 \: 5 \times 10 \times 10}}$

Collect the terms of "30" as a square of it, terms of "5" as a square of it and , terms of "10" as a square of it. Yeah it'll work.

$\bf{Area = \sqrt{30^2 \times 5^2 \times 10^2 \times 3}}$

Cancel out the squares with square root.

$\bf{Area = \sqrt{3} \: (30 \times 10 \times 5)}$

$\boxed{\bf{\therefore \: \: Area = 1500 \: \sqrt{3}}}$

HOPE THIS HELPS YOU AND STAYS AS A REFERENCE FOR OTHER STUDENTS AND CLEARS THE DOUBTS FOR APPLYING HERON'S FORMULA!!!!!!!