Question

PLEASE HELP !! 100 POINTS !! A rectangle with length 7 cm and width 9 cm is dilated by a scale factor of 2. What are the perimeter and area of the image?

Answer 1

`\boxed{\mathtt{Perimeter = 64cm.}}`

`\boxed{\mathtt{Area = 252cm^(2).}}`

Explanation:

`\textsf{We are asked to identify the area and perimeter of a dilated rectangle.}`

`\large\underline{\textsf{What is Dilation?}}`

`\textsf{\underline{Dilation} means \underline{enlarging} something by a value, which is called the \underline{scale factor}.}`

`\textsf{Because the Scale Factor is 2, we double the dimensions of the Rectangle.}`

`\mathtt{7 * 2 = 14cm \ (Length)}`

`\mathtt{ 9 * 2 = 18cm \ (Width)}`

`\textsf{Let's identify the formulas that are used for the area and perimeter of a rectangle.}`

`\mathtt{Perimeter = Length+Length+Width+Width.}`

`\mathtt{Area = Length * Width}`

`\textsf{Let's begin by Substituting.}`

`\large\underline{\textsf{Substitute:}}`

`\mathtt{Perimeter = 14cm+14cm+18cm+18cm.}`

`\boxed{\mathtt{Perimeter = 64cm.}}`

`\mathtt{Area = 14cm * 18cm}`

`\boxed{\mathtt{Area = 252cm^(2).}}`