Question

The side of an equilateral triangle drawn on a paper is 5 cm and when it is seen through a magnifier its side seems to be 10 cm.

If the ratio of the perimeter of magnified to the original is $\frac{\text{x}}{\text{y}}$, then find the value of ${\text{x}}^2-{\text{y}}^2$, [$\frac{\text{x}}{\text{y}}$ is a simple ratio].

• A. 3

Answer 1

The correct option is A 3
Perimeter of equilateral triangle = 3 $\times$ side length
[$\because$ All sides are equal]

$\frac{\text{Perimeter of magnified}}{\text{Perimeter of original}}=\frac{\text{x}}{\text{y}}=\frac{3\times 10}{3\times 5}=\frac{2}{1}$
So, x = 2 and y = 1.

[Note: Don't misintrepret that $\frac{\text{x}}{\text{y}}=\frac{2}{1}$ always implies x = 2 and y = 1, it imples only in the case of simple ratio.]

$\therefore {\text{x}}^2-{\text{y}}^2=2^2-1^2=3$