Question

how would the area be affected if the sides of rectangle are increased by a factor k?

Answer 1

How would the area be affected if the sides of rectangle are increased by a factor $k$?

Solution

Let a - one side of the rectangle, b- the second-side of the rectangle.

The area of the rectangle is calculated by the formula:

$$S = a \cdot b$$

We increase the side $a$ of a rectangle by a factor $k$ – we will get $a \cdot k$

and we will increase the side $b$ of the rectangle by a factor $k$. We'll get $b \cdot k$

Let find the area of this rectangle:

$$S = a \cdot k \cdot b \cdot k = k^2 a \cdot b$$

We can see, that area are increased by factor $k^2$

Answer: area are increased by factor $k^2$

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