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 (3)
we know that
The scale factor is equal to 2 2 1
Step 1
Convert mixed number to an improper fractions
8 2 1 in c h es = 2 8 ∗ 2 + 1 = 2 17 in c h es
2 2 1 = 2 2 ∗ 2 + 1 = 2 5
Step 2
Increasing each dimension by the scale factor
2 17 ∗ 2 5 = 4 85 in c h es
11 ∗ 2 5 = 2 55 in c h es
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 = 4 85 ∗ 2 55 = 8 4 , 675 in c h e s 2
A = 584.375 in c h e s 2
convert to mixed number
A = ( 584 + 0.375 ) in c h e s 2
A = ( 584 + 8 3 ) in c h e s 2
A = 584 8 3 in c h e s 2
therefore
the answer is
The area of the new poster is 584 8 3 in c h e s 2
Alternative Method
Let
A1--------> area of the original poster
A2------> area of the new poster
sf-------> scale factor
we know that
A 2 = A 1 ∗ ( s f ) 2
The question involves an enlarged poster with each dimension increased by a factor of 2 1/2. To find the new dimensions, we multiply each original dimension by the scale factor. The original dimensions are 8 1/2 inches by 11 inches.
The width of the enlarged poster is 8 1/2 inches × 2 1/2, which equals 21 1/4 inches ( or 8.5 inches × 2.5 = 21.25 inches ).
The height of the enlarged poster is 11 inches × 2 1/2, which equals 27 1/2 inches ( or 11 inches × 2.5 = 27.5 inches ).
To find the area of the new poster, we calculate the product of the enlarged dimensions: 21 1/4 inches × 27 1/2 inches ( or 21.25 inches × 27.5 inches ).
Mathematically, this equals to 583.4375 square inches. Therefore, the area of the enlarged poster is 583.4375 square inches.
The area of the new poster after enlarging it by a factor of 2.5 is 584 3/8 square inches. This is calculated by first enlarging the dimensions and then finding the area of the rectangle formed by the new dimensions. Therefore, the final area of the enlarged poster is 584.375 square inches or 584 3/8 square inches.
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