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# 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.

**Solution:**

Given, the perimeter of the triangular field is 420 m

The sides are in the ratio 6 : 7 : 8

We have to find the area of the triangular field.

Let the sides be

a = 6x

b = 7x

c = 8x

Perimeter = a + b + c

420 = 6x + 7x + 8x

21x = 420

x = 420/21

x = 20

a = 6(20) = 120

b = 7(20) = 140

c = 8(20) = 160

By Heron’s formula,

Area of triangle = √s(s - a)(s - b)(s - c)

Where s = semiperimeter

s = (a + b + c)/2

So, s = (120 + 140 + 160)/2

= 420/2

s = 210 cm

Area = √210(210 - 120)(210 - 140)(210 - 160)

= √210(90)(70)(50)

= √7 × 3 × 9 × 7 × 5 × 10000

= 100 × 3 × 7 (√3 × 5)

= 2100√15 cm²

Therefore, the area of the triangular field is 2100√15 cm²

**✦ Try This: **The perimeter of a triangular field is 620 m and its sides are in the ratio 5 : 4 : 8. Find the area of the triangular field.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 12

**NCERT Exemplar Class 9 Maths Exercise 12.3 Problem 7**

## 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.

**Summary:**

The perimeter of a triangular field is 420 m and its sides are in the ratio 6 : 7 : 8. The area of the triangular field is 2100√15 cm²

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