the perimeter of a triangular field is 300 cm and it's sides are in the ratio of 5:12:13. find the length of the perpendicular from the vertex to the side whose length is 130.
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The sides are in the ratio= 5:12:13
Let the sides are 5x, 12x and 13x
perimeter = 300cm
⇒ 5x+12x+13x = 300
⇒ 30x = 300
⇒ x = 300/30 = 10cm
sides are = 5×10, 12×10, 13×10 = 50cm, 120cm, 130cm
Notice that this triangle is right angled triangle with angle opposite to side 130cm as 90°. So side 50cm and 120cm are perpendicular to each other.
Area of triangle= 1/2 × 50 × 120 cm² -----------------------------(1)
Let the length of perpendicular from vertex to the side whose length is 130 be x.
So area = 1/2 × 130 × x --------------------------------(2)
From equation (1) and (2)
1/2 × 50 × 120 = 1/2 × 130 × x
⇒ 50×120 = 130×x
⇒ x = 50×120÷130
⇒ x = 46.15 cm
The length of the perpendicular from the vertex to the side whose length is 130 is 46.15cm.
Let the sides are 5x, 12x and 13x
perimeter = 300cm
⇒ 5x+12x+13x = 300
⇒ 30x = 300
⇒ x = 300/30 = 10cm
sides are = 5×10, 12×10, 13×10 = 50cm, 120cm, 130cm
Notice that this triangle is right angled triangle with angle opposite to side 130cm as 90°. So side 50cm and 120cm are perpendicular to each other.
Area of triangle= 1/2 × 50 × 120 cm² -----------------------------(1)
Let the length of perpendicular from vertex to the side whose length is 130 be x.
So area = 1/2 × 130 × x --------------------------------(2)
From equation (1) and (2)
1/2 × 50 × 120 = 1/2 × 130 × x
⇒ 50×120 = 130×x
⇒ x = 50×120÷130
⇒ x = 46.15 cm
The length of the perpendicular from the vertex to the side whose length is 130 is 46.15cm.
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