Question

Rectangle N NN has an area of 5 55 square units. James drew a scaled version of Rectangle N NN and labeled it Rectangle P PP. Rectangle P Rectangle P What scale factor did James use to go from Rectangle N NN to Rectangle P PP?

Answer 1

The scaled factor is 3.

Explanation:

Consider the figure shown below:

It is given that: A rectangle N has an area of 5 square units. James drew a scaled version of Rectangle N and labeled it Rectangle P.

We need to find the scale factor which is used by James.

First, we will calculate the area of Rectangle P by counting the number of squares shown in the figure.

Area of rectangle P = 45 square unit

Let x be the scaled factor.

To scale the rectangle we need to multiply both the length and breadth of the rectangle N by x and the scaled area should be equal to 45.

`[x* \text{Length} ][x * \text{breadth}]=45`

`x^2(\text{Length} * \text{breadth})=45`

It is given that area of the rectangle N is 5 square units, so put length time breadth as 5.

`x^2(5)=45`

`x^2=9`

`x=3`

Hence, the scaled factor is 3.