Question

The altitude of a triangle is two-third the length
of its corresponding base. If the attitude increased
by 4 cm and the base decreased by 2 cm, the area
of the triangle remains the same. Find the base
and the altitude of the triangle.
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Answer 1

Answer:

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Answer 2

Answer: 2

Step-by-step explanation:

Let x be the base. Altitude is 2x/3.

Area = 0.5(x*2x/3) = x²/3

Now let new base and height be x-2 and 2x/3 + 4.

Area = 0.5(x-2)(2x/3 + 4) = 2x²/3 + 8x/3 -8

Since areas are same,

x²/3 =x²/3 + 4x/3 -4

Solving we get x = 3

Therefore altitude = (2/3).3= 2