Question

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

READ THE QUESTION PROPERLY I want the full answer WITH the area of the field.

Answer 1

ANSWER

let the sides are 6x, 7x,8x

now ...

6x+7x+8x=420

x=420/21=20

therefore the sides are 120m,140m,160m

now ,half perimeter=420/2=210m

now area

$\sqrt{210(210 - 120)(210 - 140)(210 - 160)} \: m {}^{2} \\ \sqrt{210 \times 90 \times 70 \times 50 } \\ \sqrt{3 \times 7 \times 3 \times 3 \times 7 \times 5 \times 10000} \\ 2100 \sqrt{15} \: m {}^{2}$

Answer 2

》Solution《

●explanation

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.

Perimeter of a triangular field, 2s = a + b + c ⇒ 420 = 6x + 7x + 8x ⇒ 420 = 21x

Perimeter of a triangular field, 2s = a + b + c ⇒ 420 = 6x + 7x + 8x ⇒ 420 = 21x⇒ x = 420/21 = 20 m.

■answer:-20metre

now a = 6 × 20 =120m

b= 7 × 20 =140 m

c = 8 × 20 =160 m

hence ,perimetre = 120 + 140 +160 = 420

now find semi perimetre then find the area of triangle by using herons formula