Question

A teacher has a model of an L shaped building made of four cubes that snap together. She wants to make an enlargement similar in shape to the original. She only has 600 cubes. What scale factor should she use to make the largest building possible explain your reasoning.

Answer 1

Ans. The scale factor should be 1 : 150.

Logical Reason:

When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles.

Here the model of the L shaped building and the original enlarged building are similar to each other.

In this case, Let us assume the edge of the cube to be 1unit, then the area of the cube will be 1u² .

In the model of the L-shaped building there are 4 cubes, therefore its area would be 4 u²

The original L-shaped building is made up of 600 cubes. Therefore the area of the original building would be 600 u²

When the area of the model building is similar to the area of the original enlarged building.

Then, Area of the model : Area of the original = 4 u² : 600 u²(Ratio of areas of similar structures is in direct variation)

                                            Ratio of Areas = 1 : 150.

Therefore the scale factor for the making of largest building possible can be 1 : 150.