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?

Question

asked Jan 27, 2015 85.7k views

1 Answer

Shiori · Answer 1 · 2015-02-01T04:59:41+0000

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)