Similarity and enlargement

Juliana says, 'All of these three shapes are similar.' Do you think she is correct? Explain your answer:

In each pair of similar shapes, work out the missing side length and explain how you calculated them.

George has produced a logo design for his dad's company. They want to use the design, but have to enlarge it by a scale factor of two. Draw the enlarged shape below and explain how you completed it.

This picture shows two triangles: triangle ACD and triangle ABE. They are similar triangles. Calculate the length of the side AD

(a)  

Two bottles are mathematically similar. The height of one is 10cm and the height of the other is 20cm. If the smaller bottle has a capacity of 500ml, what is the capacity of the larger bottle?

• 4L

• 2L

• 125ml

• 1L

Here are the dimensions of a field. The field has a grassed area in the middle, ditch around the grass and a fence around the outside of the ditch. The distance from the edge of the grass to the edge of the ditch is equal around the field. A farmer has another field which is an enlargement of this field by e scale factor of two (both grassed area and ditch are enlarged). How much fencing would the farmer need to put a fence around the outer edge of the ditch of the larger field?

(a)  

Enlarge the rectangle by a scale factor of 1.5 then calculate the area of the shape.

(a)  

Two glasses are mathematically similar. Pouring water at the same rate, it takes 5 seconds to fill the smaller glass and 40 seconds to fill the larger glass. If the height of the smaller glass is 10cm, what is the height of the larger glass?

• 40cm

• 20cm

• 5cm

• 80cm

In each pair of similar shapes, work out the missing side length and explain how you calculated them.

In each pair of similar shapes, work out the missing side length and explain how you calculated them.