Question

Noah enlarged a rectangular photograph by a scale of 6. The area of the enlarged photo is how many times as large as the originalOptions: 6 times larger 12 times larger 30 times larger36 times larger

Answer 1

The area of a rectangle is the product of the length and the breadth of the rectangle.

lets assume the initial length and breadth of the rectangle are l and b, the initial area will then be;

$\begin{gathered} A=l\times b \\ A=lb \end{gathered}$

When the rectangle is enlarged by 6 the initial length and breadth are both increase to a multiple of 6;

$\begin{gathered} l\rightarrow6l \\ b\rightarrow6b \end{gathered}$

So, the final area will be;

$\begin{gathered} A_f=6l\times6b \\ A_f=36lb \end{gathered}$

Substituting A =lb from the first initial area, we have;

$\begin{gathered} A_f=36lb=36A \\ A_f=36A \end{gathered}$

Therefore, the area of the enlarged photo is 36 times the original.