Home
Class 9
MATHS
The perimeter of a triangular field is 4...

The perimeter of a triangular field is `420` `m` and its sides are in the ratio `6` : `7` : `8`. Find the area of the triangular field.

Text Solution

Verified by Experts

Given, perimeter of a triangular field is 420 m and its sides are in the ratio 6:7:8.
Let sides of a triangular field be a=6x, b=7x and c=8x.
`therefore"Perimeter of a triangular field",2s=a+b+c`
`rArr" "420=6x+7x+8xrArr420=21x`
`rArr" "x=(420)/(21)=20m`
`therefore"Side of a triangular field are"`
`therefore"Side of a triangular field are"`
`a=6xx20=120m`
`b=7xx20=140m`
`"and"" "c=8xx20=160m.`
`"Now"," ""semi-perimeter", S=(a+b+c)/(2)=(120+140+160)/(2)`
`=(420)/(20)=210m`
`therefore"Area of a triangular field"=sqrt(s(s-a)(s-b)(s-c))" "["by Heron's formula"]`
`=sqrt(210(210-120)(210-140)(210-160))`
`=sqrt(210xx90xx70xx50)`
`100=sqrt(21xx9xx7xx5)`
`100=sqrt(7xx3xx3^(2)xx7xx5)`
`=100xx7xx3xxsqrt15=2100sqrt15m^(2)`
Hence, the area of triangular field is `2100sqrt15m^(2)`.
Promotional Banner

Topper's Solved these Questions

  • HERON'S FORMULA

    NCERT EXEMPLAR ENGLISH|Exercise Long Answer Type Questions|8 Videos

  • HERON'S FORMULA

    NCERT EXEMPLAR ENGLISH|Exercise Very Short Answer Type Questions|9 Videos

  • COORDINATE GEOMETRY

    NCERT EXEMPLAR ENGLISH|Exercise Exercise 3.4 Long Answer Type Questions|5 Videos

  • INTRODUCTION TO EUCLID GEOMETRY

    NCERT EXEMPLAR ENGLISH|Exercise Exercise 5.4 Long Answer Type Questions|5 Videos

Similar Questions

Explore conceptually related problems

The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of the triangle.

The perimeter of a triangular field is 450\ m and its sides are in the ratio 13 : 12 : 5. Find the area of the triangle.

The perimeter of a triangular field is 450\ m and its sides are in the ratio 13 : 12 : 5. Find the area of the triangle.

The perimeter of a triangular field is 540 m and its sides are in the ratio 25: 17:12 . Find the area of the triangle. Also, find the cost ploughing the field at Rs. 18.80 per 10 m^2

The perimeter of a triangle is 450 m and its sides are in the ratio 12 : 5 : 13 . Find the area of the triangle.

The perimeter of a triangle is 540 m and its sides are in the ratio 12 : 25 : 17. Find the area of the triangle.

The perimeter of a triangle is 300 mdot If its sides are in the ratio 3:5: 7. Find the area of the triangle.

The perimeter of a triangular field is 144 m and the ratio of the sides is 3:4:5. Find the area of the field.

The perimeter of a rectangular field is 216 metres and its breadth is 40 metres . Find the length and area of the rectangle.

The perimeter of a triangular field is 240dm. If two of its sides are 78dm and 50dm, find the length of the perpendicular on the side of length 50dm from the opposite vertex.