The perimeter of a triangle field is 300 cm and its sides are in the ratio 5 : 12 :13. Find the length of the perpendicular from the opposite vertex to the side whose length is 30 cm.
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Given sides of triangles are in the ratio 5:12:13 Let the sides be 5x, 12x and 13xPerimeter of triangle = 300 cm ⇒ 5x + 12x + 13x = 300 ⇒ 30x = 300 ∴ x = 10Hence the sides of the given triangle are 50 cm, 120 cm and 130 cm Notice that 1302 = 502 + 1202 ⇒ 16900 = 2500 + 14400 = 16900 Thus the given triangle is a right angled triangle with hypotenuse 130 cm and the perpendicular sides are 50 cm and 120 cm.
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300=5x+12x+13x
300=30x
x=10
300=30x
x=10
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