Question

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?

Answer 1

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

Step-by-step 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

`\begin{gathered} b=\sqrt[]{20} \\ b=2\sqrt[]{5}\text{ in} \end{gathered}`

Increase the original side by a scale factor of 4

`b1=4(2\sqrt[]{5})\text{ in}`

Find the new area

A1=b1^2

substitute the new value of b1

`\begin{gathered} A1=\lbrack8\sqrt[]{5})^2 \\ A1=64\cdot5 \\ A1=320\text{ in2} \end{gathered}`

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

the enlarged area is 36 times the area of the original