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Use Ratios to Find Scale Factors and Missing Lengths

In this worksheet, students will solve problems involving similar shapes where the scale factor is known or can be found.

'Use Ratios to Find Scale Factors and Missing Lengths' worksheet

Key stage:  KS 2

Curriculum topic:   Ratio and Proportion

Curriculum subtopic:   Solve Shape Problems

Difficulty level:  

Worksheet Overview

Similar shapes have matching corresponding angles and corresponding sides which are in the same ratio.

 

Similar triangles

 

In these two triangles, the angles match and you will notice that the second triangle has sides which are double the length of the sides of the first triangle.

The ratio of the bases is 3:6, which simplifies like a fraction to 1:2.

The ratio of the heights is 7:14, which simplifies like a fraction to 1:2.

 

 

Example

These two rectangles are similar.

Find the missing length.

 

Similar rectangles

 

Answer

The ratio of the bases is 4:8, which simplifies to 1:2.

The big rectangle's sides are 2 times the matching sides of the small rectangle.

The missing side is 2 × 5 = 10 cm.

 

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