Question

Fill in the blank:

The ratio of the areas of two similar triangles is equal to the _______ of the ratio of their corresponding sides.

• A. square
• B. twice
• C. four times
• D. none of these

Answer 1

The correct option is A square

Given : $△ABD\sim △EFH$

$\therefore \frac{AB}{EF}=\frac{BD}{FH}=\frac{AD}{EH}$ ...C.S.S.T ...(1)

Now, $A\left(△ABD\right)=\frac{1}{2}\times BD\times AD$

And, $A\left(△EFH\right)=\frac{1}{2}\times FH\times EH$

$\therefore \frac{A\left(△ABD\right)}{A\left(△EFH\right)}=\frac{\frac{1}{2}\times BD\times AD}{\frac{1}{2}\times FH\times EH}$

$\therefore \frac{A\left(△ABD\right)}{A\left(△EFH\right)}=\frac{BD}{FH}\times \frac{AD}{EH}$

Hence, $\frac{A\left(△ABD\right)}{A\left(△EFH\right)}=\frac{BD}{FH}\times \frac{BD}{FH}$ ....From (1)

$\therefore \frac{A\left(△ABD\right)}{A\left(△EFH\right)}={\left(\frac{BD}{FH}\right)}^2$