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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
Solution
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
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