Q. 74.0( 21 Votes )
The base of a triangle is 4cm longer than its altitude. If the area of the triangle is 48 sq.cm, the find its base and altitude.
Answer :
let the base of the triangle be x cm and altitude be y cm
Given base = 4 + y
Area of the triangle = 1/2 × base × altitude
48 = 1/2 × (4 + y) × y
⇒ 96 = 4y + y2
⇒ y2 + 4y – 96 = 0
⇒ y2 + 12y - 8 y – 96 = 0
⇒ y( y + 12) - 8 ( y + 12) = 0
⇒ (y - 8) ( y + 12) = 0
⇒ y = 8 or - 12
Since altitude cannot be negative ∴ y = 8
⇒ base = 4 + 8 = 12 cm
Hence, Base = 12 cm; Altitude = 8 cm
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