Question

Q7. The perimeter of a triangle is 240cm. If two of its sides are 78cm and 50cm. Find the length of
perpendicular corresponding to the smallest side​

Answer 1

I hope my answer is correct

Answer 2

Given : The perimeter of a triangle is 240 cm. two of its sides are 78 cm and 50 cm.

To find : the length of perpendicular corresponding to the smallest side.

solution : perimeter = sum of all sides

⇒240 cm = 78cm + 50cm + 3rd side

⇒240 - 128 = 3rd side

⇒3rd side = 112 cm

therefore smallest side is 50cm.

now we have find length perpendicular drawn to smallest side ( i.e., 50 cm)

if ABC is triangle where AB = 78cm, BC = 50cm and AC = 112 cm. one altitude is drawn from A to BC as shown in figure. hence AT is altitude

so area of Triangle ABC = 1/2 × BC × AT

⇒√{s(s - a)(s - b)(s- c)} = 1/2 × 50 × AT

⇒√{120(120 - 78)(120 - 50)(120 - 112)} = 25 × AT

⇒√{120 × 42 × 70 × 8} = 25 × AT

⇒1680/25 = AT

⇒AT = 67.2 cm

Therefore the length of perpendicular to the smallest side is 67.2 cm