Question

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?

Answer 1

Answer:

1.96 : 1

Step-by-step explanation:

The area of a triangle is  

$A=\frac{1}{2}bh$

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  $A=\frac{1}{2}bh$

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:

$A=\frac{1}{2}(1.4b)(1.4h)\\A=\frac{1}{2}(1.4*1.4)bh\\A=\frac{1}{2}bh*1.96$

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:

$\frac{\frac{1}{2}bh(1.96)}{\frac{1}{2}bh}\\=1.96:1$

So the ratio is 1.96:1