Question

In triangle $ABC,\overline{AB}=12,\overline{AC}=7$, and $\overline{BC}=10$. If sides $AB$ and $AC$ are doubled while $BC$ remains the same, then

• A. The area is doubled
• B. The altitude is doubled
• C. The area is four times the original area
• D. The median is unchanged
• E. The area of the triangle is $0$

Answer 1

Answer: (E)

The area of the triangle is $0$

In the new triangle $\overline{AB}=\overline{AC}+\overline{BC}$, that is, $C$ lies on the line $AB$. Consequently, the altitude from $C$ is zero. Therefore, the area of the triangle is zero.