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Question: By how many times will the area of a triangle increase, if the base and the height are increased by 3 times?


A ) 3 times
B ) 9 times
C ) 12 times
D ) 4 times

Steps to derive

1 Let h be the height of the triangle and b be the base of the triangle.

2 The area of the triangle = 12 x b x h

3 The length of the base and the length of the height are increased by 3 times.

4 The new base is 3 x b and the new height is 3 x h.

5 The new area of the triangle = 12 x (3 x b) x (3 x h)

6 = 9 x (12 x b x h)

7 = 9 x original area of the triangle

8 The area of the triangle increases by 9 times.



Hence the right answer is Option B

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