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 :

we know that

The scale factor is equal to [tex]2\frac{1}{2}[/tex]

Step 1

Convert mixed number to an improper fractions

[tex]8\frac{1}{2}\ inches=\frac{8*2+1}{2} =\frac{17}{2}\ inches[/tex]

[tex]2\frac{1}{2}=\frac{2*2+1}{2} =\frac{5}{2}[/tex]

Step 2

Increasing each dimension by the scale factor

[tex]\frac{17}{2}*\frac{5}{2}=\frac{85}{4}\ inches[/tex]

[tex]11*\frac{5}{2}=\frac{55}{2}\ inches[/tex]

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

[tex]A=\frac{85}{4}*\frac{55}{2}=\frac{4,675}{8}\ inches^{2}[/tex]

[tex]A=584.375\ inches^{2}[/tex]

convert to mixed number

[tex]A=(584+0.375)\ inches^{2}[/tex]

[tex]A=(584+\frac{3}{8})\ inches^{2}[/tex]

[tex]A=584\frac{3}{8}\ inches^{2}[/tex]

therefore

the answer is

The area of the new poster is [tex]584\frac{3}{8}\ inches^{2}[/tex]

Alternative Method

Let

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

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

sf-------> scale factor

we know that

[tex]A2=A1*(sf)^{2}[/tex]