Question

the area of a triangle is 30 cm sq . find the base if the altitude exceeds the base by 7cm

Answer 1

Let the length of base = P cm.
As base exceeds the base by 7cm ,
then , length of altitude = (P + 7)cm

now, area of triangle = 1/2 × altitude × base

given, area of triangle = 30 cm²

so, 30 cm² = 1/2 × (P + 7) × P

=> 30 × 2 = P² + 7P

=> 60 = P² + 7P

=> P² + 7P - 60 = 0

=> P² + 12P - 5P - 60 = 0

=> P(P + 12) - 5(P + 12) = 0

=> (P + 12)(P -5) = 0

=> P = 5 , -12

but length can't be negative so, P ≠ -12

hence, P = 5 cm e.g., base = 5cm

Answer 2

Answer:

30 cm² = 1/2 × (P + 7) × P

30 × 2 = P² + 7P

60 = P² + 7P

P² + 7P - 60 = 0

P² + 12P - 5P - 60 = 0

P(P + 12) - 5(P + 12) = 0

(P + 12)(P -5) = 0

P = 5 , -12

but length can't be negative so, P ≠ -12

hence, P = 5 cm e.g., base = 5cm