Question

The perimeter of a triangular field is 300cm & its side are in ratio 5:12:13 find the length of perpendicular from opposite vertex to side whose length is 130m

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

Answer 2

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.