Question

find the percentage increase in the area of a triangle if its side is doubled​

Answer 1

In similar triangles, ratio of areas is equal to ratio of the square of corresponding sides. When sides are doubled, the area of new triangle will always be 4 times the original, the change in area will be 3 times. Hence the % change will always be 300% irrespective of the type of triangle.

Answer 2

Initial side of triangle = b

Let height = h

Earlier area of the triangle = ½×b×h

Increased side (B) = 2b

Area after increase = ½×B×h

= ½×2b×h

Increase = (½2bh)-(½bh)

= ½bh(2-1)

= ½bh

Increase % = ½bh/½bh×100

= 100%

Increase Percentage = 100%

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