Question

A picture is 5 inches wide and 8 inches tall.

A photographer wants to use a scale factor of 2.5 to enlarge a picture. What will the area of the picture be after it is enlarged?


40 in²


250 in²


100 in²


81.9 in²

Answer 1

`\large\boxed{\tt Area=250in.^(2)}`

Explanation:

`\textsf{We are asked for the area of a Dilated Rectangle.}`

`\textsf{We are given the dimensions, 5 inches wide and 8 inches in length. Then, we are}`

`\textsf{given a \underline{Scale Factor}.}`

`\large\underline{\textsf{What is a Scale Factor?}}`

`\textsf{A Scale Factor is a term that represents how large the next shape will be. Note}`

`\textsf{that only sides of a shape are affected by the Scale Factor. Angles, and the form}`

`\textsf{of the shape remain the same.}`

`\underline{\textsf{Example;}}`

`\textsf{We are given a rectangle with 5 cm. as the length, and 6 cm. as the width.}`

`\textsf{The Scale Factor is 2.}`

`\textsf{We will multiply the dimensions of the triangle by 2, then find the area.}`

`\large\boxed{\tt Area = Length * Width}`

`\tt Area=(5 * 2) * (6 * 2)`

`\tt Area=10 * 12`

`\large\boxed{\tt Area=120cm^(2)}`

`\large\underline{\textsf{For our problem;}}`

`\textsf{We should start solving for the dilated area after multiplying the dimensions by}`

`\textsf{the Scale Factor.}`

`\textsf{Remember That You Should Not Multiply The Scale Factor By The Area.}`

`\large\underline{\textsf{Solving;}}`

`\textsf{Multiply the dimensions by the Scale Factor.}`

`\tt Area=(5 * 2.5) * (8 * 2.5)`

`\underline{\textsf{This will evaluate to;}}`

`\tt Area=12.5 * 20`

`\large\boxed{\tt Area=250in.^(2)}`