Similarity of polygons
Answers are for parents and teachers.
1
A rectangle 14 cm × 10 cm is similar to a rectangle 21 cm long. Find its width.
14 ÷ 21 = 2/3, so the width is 10 × 3/2 = 15 cm.
2
A pentagon has perimeter 36 cm and longest side 10 cm. A similar pentagon has longest side 25 cm. Find its perimeter.
k = 10 ÷ 25 = 2/5, so the perimeter is 36 × 5/2 = 90 cm.
3
A rhombus of side 5 cm with a 60° angle and a rhombus of side 8 cm with a 120° angle: are they similar? Find k.
Yes: each has angles 60° and 120°. k = 5 ÷ 8.
4
A photo 30 cm × 20 cm is enlarged to 45 cm long. Find the new width and the ratio of the perimeters.
k = 30 ÷ 45 = 2/3, so the width is 20 × 3/2 = 30 cm. Perimeters 100 cm and 150 cm: ratio 2/3.
5
Why are a square and a rhombus that is not a square never similar, even though all their sides are equal?
The side ratios are all equal, but the angles are not: a square has four 90° angles and a rhombus that is not a square does not.