Question

For a scale factor less than 2, the ratio of the area of triangle to be constructed and the triangle given will be always

• A. 2
• B. Less than 2
• C. Less than 4
• D. Greater than 4
  

Answer 1

The correct option is C Less than 4

Let $\Delta ABC$ be the given triangle and $\Delta A\text{'}BC\text{'}$ to be constructed similar to $\Delta ABC$.


Then,$\frac{areaof\Delta A^{\prime }{B}^{\prime }{C}^{\prime }}{areaof\Delta ABC}=\left(\frac{A^{\prime }B}{AB}\right)<\left(2{)}^2\right(\because \text{Scale factor is less then 2})$
$\frac{areaof\Delta A^{\prime }{B}^{\prime }{C}^{\prime }}{areaof\Delta ABC}<4$

Thus, for a scale factor less than 2, the ratio of the area of the triangle to be constructed and the triangle given will be always less than 4.

Hence, the correct answer is option c.