Question

The perimeter of a triangular field is 390m and its sides are in the ratio 5 :12:13. Find the length of the altitude corresponding to the longest side.

Answer 1

Answer:

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.

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Answer 2

Answer:

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.