If side of a scalene a is doubled then area would be increased by
a. 200%
b. 25 %
c. 50%
d. 300 %
Answers
Answer:
As I type this, the other two answers both approach the problem using Heron’s formula, to adjust a calculation of the area based on the length of the three sides. This approach, while accurate, is significantly more labor-intensive than is strictly necessary to answer the question.
If you have a plane figure – doesn’t even matter if it’s a triangle, or even a polygon – and you double every linear measurement – in this case, all three sides — then you’ve created a similar figure with linear scale factor of two.
The area of a similar figure scales as the square of the linear scale factor – so for these triangles, k=2 and k2=22=4 . Thus, the new area is 4 times the original area, or 400% of the original area — an increase of 300%.