3 years ago

The ratio of the areas of two similar rectangles is 1:4. What is the ratio of the corresponding sides?

1 answer:

4 0

The ratio of linear dimensions (side lengths) is the square root of the ratio of areas.
√1 : √4 = 1 : 2

The best choice is ...
B. 1:2

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Maurinko [17]

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$\mathbf v=(\vec i+\vec j+\vec k)\times(4\,\vec i+\vec k)=\begin{vmatrix}\vec i&\vec j&\vec k\\1&1&1\\4&0&1\end{vmatrix}=\vec i+3\,\vec j-4\,\vec k$

Normalize this vector by dividing it by its norm:

$\dfrac{\mathbf v}{\|\mathbf v\|}=\dfrac{\vec i+3\,\vec j-4\,\vec k}{\sqrt{1^2+3^2+(-4)^2}}=\dfrac1{\sqrt{26}}(\vec i+3\,\vec j-4\vec k)$

To get another vector orthogonal to the first two, you can just change the sign and use $-\mathbf v$ .