Question

A poster is 8 1/2 inches by 11 inches. You enlarge the poster by increasing each dimension by a factor of 2 1/2. What is the area of the new poster?

Answer 1

we know that

The scale factor is equal to
`2(1)/(2)`

Step 1

Convert mixed number to an improper fractions

`8(1)/(2)\ inches=(8*2+1)/(2) =(17)/(2)\ inches`

`2(1)/(2)=(2*2+1)/(2) =(5)/(2)`

Step 2

Increasing each dimension by the scale factor

`(17)/(2)*(5)/(2)=(85)/(4)\ inches`

`11*(5)/(2)=(55)/(2)\ inches`

Step 3

Find the area of the new poster

we know that

the area of the poster is equal to find the area of a rectangle

`A=(85)/(4)*(55)/(2)=(4,675)/(8)\ inches^(2)`

`A=584.375\ inches^(2)`

convert to mixed number

`A=(584+0.375)\ inches^(2)`

`A=(584+(3)/(8))\ inches^(2)`

`A=584(3)/(8)\ inches^(2)`

therefore

the answer is

The area of the new poster is
`584(3)/(8)\ inches^(2)`

Alternative Method

Let

A1--------> area of the original poster

A2------> area of the new poster

sf-------> scale factor

we know that

`A2=A1*(sf)^(2)`