Question

The perimeter of a triangular plot is 600 m. If the sides are in the ratio 5 : 12 : 13, then find the area of the plot

Answer 1

Let the side of the triangle a, b and c be 5x, 12x and 13x

Perimeter of a triangular plot = 600 m

5x + 12x + 13x = 600

30x = 600

⇒ x = `600/30`

x = 20

a = 5x = 5 × 20 = 100 m

b = 12x = 12 × 20 = 240 m

c = 13x = 13 × 20 = 260 m

s = `600/2`

= 300 m

s – a = 300 – 100 = 200 m

s – b = 300 – 240 = 60 m

s – c = 300 – 260 = 40 m

Area of triangle

= `sqrt("s"("s" - "a")("s" - "b")("s" - "c"))`

= `sqrt(300 xx200 xx 60 xx 40)`

= `sqrt(3 xx 2 xx 6 xx 4 xx 100 xx 100 xx 100)`

= `sqrt(3 xx 2 xx 2 xx 3 xx 2^2 xx 10^6)`

= 10³ × 3 × 2 × 2 m²

= 1000 × 12 m²

= 12000 m²

Area of the triangular Plot = 12000 sq.m