Question

One side of square A is a diagonal of Square B What is the ratio of the area of square B to the area of Square A? Express and answer as common fraction.

Answer 1

check the picture below.

so if each side of square A is x long, its area is then x*x or namely x².

now, we know the diagonal of square B is x long, so let's find how long is each side, namely how long is y.

`image`

`\bf \cfrac{\textit{area of B}}{\textit{area of A}}\implies \cfrac{\quad (x^2)/(2)\quad }{x^2}\implies \cfrac{\quad (x^2)/(2)\quad }{(x^2)/(1)}\implies \cfrac{x^2}{2}\cdot \cfrac{1}{x^2}\implies \cfrac{1}{2}`