Q28 of 168 Page 7

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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