Question

The vertices of the inscribed (inside) square bisect the sides of the second (outside) square. Find the ratio of the area of the outside square to the area of the inscribed square.

3:1
1:3
4:1
2:1​

Answer 1

Question -

The vertices of the inscribed(inside) square bisect the sides of the second (outside) square. Find the ratio of the area of the outside square to the area of the inscribed square

Solution

Let 2 x be the size of the side of the large square

The area of the large square is

(2 x ) × ( 2x) = 4 x²

The area of the inscribed square is

y × y = y²

Use of Pythagoras theorem gives-

y² = x² + x²

= 2x²........1)

Ratio R of the area of the outside square to the area of the inside square is given by

$R = \frac{4 {x}^{2} }{y}$

$R= \frac{4 {x}^{2} }{2 {x}^{2} } (by \: 1)$

$R = \frac{4}{2}$

$R = \frac{2}{1}$

$R = 2\ratio1$

Answer is 2:1