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

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 =

given, area of triangle = 30 cm2

so,

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

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