Question

The base of a triangle with area 30 cm² and height 3 cm is *

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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

hope it helps you

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