Question

A rectangle with an area of 20 square units is dilated by the scale factor of 3.5. find the area of the new rectangle

Answer 1

We are given the area of a rectangle. The area of a rectangle is the product of the length and the height. Therefore, we have:

`A=lh`

If we scale the rectangle by a factor of 3.5 this means that we multiply the length and the height by 3.5, like this:

`A^(\prime)=(3.5l)(3.5h)`

Solving the product:

`A^(\prime)=12.25lh`

Since "lh" is the original area we have:

`A^(\prime)=12.25A`

Now, we substitute the value of the original area:

`A^(\prime)=12.25(20)`

Solving the operations:

`A^(\prime)=245`

Therefore, the new area is 245 square units.