[4 times] By how many times will the area of a triangle increase, if the base and the height are increased by

For Competitive Exams

By how many times will the area of a triangle increase, if the base and the height are increased by 2 times?

3 times

4 times

5 times

6 times

Explanation:

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

The area of the triangle A=$\dfrac{1}{2}$bh

The length of the base and the length of the height are increased by 2 times.

The new base is $2 \times b $ and the new height is $ 2 \times h.$

The new area of the triangle = $\dfrac{1}{2} \times (2 \times b) \times (2 \times h)$

= 4 $\left(\dfrac{1}{2}bh\right)$

= 4 × original area of the triangle

The area of the triangle increases by 4 times.

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