Respuesta :
Lin has a drawing with an area of 20 in². if she increases all the sides by a scale factor of 4, what will the new area be?
Remember that
the ratio between similar areas is equal to the scale factor squared
so
that means
scale factor=4
x/20=4^2
where
x is the new area
x/20=16
x=320 in2
the new area is 320 square inches
Explanation
assume that the original figure is a square
A=20 in2
the area of a square is
A=b^2
Find out the length b
[tex]\begin{gathered} b=\sqrt[]{20} \\ b=2\sqrt[]{5}\text{ in} \end{gathered}[/tex]Increase the original side by a scale factor of 4
[tex]b1=4(2\sqrt[]{5})\text{ in}[/tex]Find the new area
A1=b1^2
substitute the new value of b1
[tex]\begin{gathered} A1=\lbrack8\sqrt[]{5})^2 \\ A1=64\cdot5 \\ A1=320\text{ in2} \end{gathered}[/tex]that is the same that multiply the original area by the scale factor squared
Problem N 2
Remember the problem N 1
the ratio between similar areas is equal to the scale factor squared
in this problem
the scale factor=6
(scale factor )^2=6^2=36
that means
