Question

The perimeter of a triangular field is 36m and the ratio of the sides is 8:5:5. The area of the field in sq m is

Answer 1

$let \: the \: sides \: be \: 8x, \: 5x, \: 5x \\ \\ ATQ \\ \\ = > 8x + 5x + 5x = 36 \\ \\ = > 18x = 36 \\ \\ = > x = \frac{36}{18} \\ \\ = > x = 2 \\ \\ 8x = 8 \times 2 = 16m \\ 5x = 5 \times 2 = 10m \\ 5x = 5 \times 2 = 10m$

Answer 2

Ratio of sides = a : b : c = 8 : 5 : 5

a = 8k

b = 5k

c = 5k

Perimeter of triangle = a + b + c = 36m

36 = 8k + 5k + 5k

18k = 36

k = 2

a = 8 × 2

a = 16

b = 5 × 2

b = 10

c = 5 × 2

c = 10

s = a + b + c / 2

s = 16 + 10 + 10 / 2

s = 36 / 2

s = 18

area of triangle = √[s (s-a) (s-b) (s-c)]

area of triangle = √[18 (18-16) (18-10)

(18-10)]

area of triangle = √(18 × 2 × 8 × 8)

area of triangle = √(36 × 64)

area of triangle = 48m^2

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