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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