This problem solving activity has a geometry focus.
Sol is at a party and has a serviette folded into an isosceles triangle.
On the table are two square flower vases.
Although these are different sizes, they both fit on the serviette - one one way and then the other the other way.
He notices that the bigger vase A has a side length of 21cm.
What is the side length of the smaller vase?
This problem involves students exploring the area of isosceles triangles and related squares.
It is possible to solve this problem using using a scale drawing. Students should be encouraged to be accurate in their drawing and to notice how the isosceles triangle can be dissected to fit into the squares in the diagram. However, it’s worth noting that, generally speaking, scale diagrams can only give approximations to the ‘real’ thing. Therefore, it is almost always necessary to do something more sophisticated to get an accurate answer. On the other hand, scale diagrams may give clues to the exact answer (see Rings and Diamonds, Geometry, Level 5) and there may be some situations where scale diagrams give sufficient accuracy for more sophisticated methods not to be worthwhile. As a general rule, only use scale diagrams when everything else has been tried.
Note: In Bill’s Badge, Measurement, Level 5 students also break up an area to enable particular information to be found.
Sol is at a party and has a serviette folded into an isosceles triangle. On the table are two square flower vases. Although these are different sizes, they both fit on the serviette - one one way and then the other the other way.
He notices that the bigger vase A has a side length of 21cm. What is the side length of the smaller vase?
Because the serviette is isosceles, the larger square (vase A) is ½ of the area of the triangle. Using the side length of 21cm, we can calculate the area of the triangle as 2 x (21)2 = 882 (cm2).
The other diagram can be redrawn as below.
From this diagram, we can see that the triangle is made up of all 9 small triangles and the smaller square is made up of 4 small triangles. So the area of the smaller square is
4/9 x 882 = 392 cm2.
This gives the side of the smaller square as √392 = 19.80 cm.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/sol-s-serviettes at 8:58pm on the 26th February 2024