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Question

The base of a triangle is 4 cm longer than its altitude. If the area of the triangle is 48 sq. cm, then find its base and altitude.

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Solution

Let the altitude of the triangle be x cm.
By the given condition, the base of the triangle is (x + 4) cm.
Now, the area of the triangle = 12(base)×(height)
By the given condition 12(x+4)(x)=48
x2+4x96=0(x+12)(x8)=0
x=12 or 8
But x = 12 - is not possible (since the length should be positive)
Therefore, x = 8 and hence, x+4=12.
Thus, the altitude of the triangle is 8 cm and the base of the triangle is 12 cm.

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