Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
Stage: 2 Challenge Level:
Kerr, Lewis,Sophie and Holly from Dundonald
School have been working on this problem. They saw that the ratio
of the blue rod to the black rod is 9:7.
Well done to Isis (South Island School),
Rohaan (Long Bay Primary) and Samantha (The Hamlin School) for
completing this toughnut! Samantha explained how she manged to find
a pair with the same ratio as the yellow and pink rods:,
"The pink rod had 4 units and the yellow one had 5 units. This
meant that they had a ratio of 4:5. I then needed to find a like
ratio. This can be done by multiplying both numbers in the ratio by
the same number. In this case the number had to be 2 because the
longest rod is 10 units. So the 8 (brown colored) and the 10
(orange colored) rods would have the same ratio as the 4 (pink
colored) and the 5 (yellow colored)"
She also found pairs with the same ratio as
the combined yellow+orange, to the blue rod:
The ratio of yellow (5) + orange (10) to blue (9) is equal to the
ratio 15 to 9. This ratio can be simplified to a 5:3 ratio by
dividing both 15 and 9 by 3. Therefore, the yellow and green rods form an equal
ratio to that of the yellow + orange to the blue. Another equal
ratio would be 10 to 6. Therefore, the dark green and orange rods also form an
Finally she noted that the rods with the
same ratio as 9:6 have already been given!
"The ratio of 9:6 can be simplified to the ratio 3:2. The possible
combinations with rods for that ratios are shown at the start of
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