The side lengths of triangle a are increased by 40%. the side lengths of triangle b do not change. what is the new ratio of the area of triangle a to triangle b?

1.96 : 1

Step-by-step explanation:

The area of a triangle is  

Where b is the base and h is the height

Since triangle b's side do not change, let base be b and height be h, so area would simply be  

Since side lengths are increased by 40%, that means:

40% = 40/100 = 0.4

Increase of this means "multiply by 1.4"

So base will increase by this as well as height. So with respect to triangle b, triangle a's area would be:

So, there's an extra factor of 1.96 which means area increased by 96%!

So, we find ratio of triangle a to triangle b (area) by dividing area of triangle a to triangle b:

So the ratio is 1.96:1

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