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The Tree and the Greenhouse

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Conor from Sticklepath School decided to estimate the height of the tree:

If the bamboo cane was exactly 1m (100cm) and the length of the shadow was 123cm then that means that the shadow is 23cm longer than the bamboo cane is.
23cm is about 1/5 more than 100cm (the length of the bamboo cane).
1/5 of 36.3m (the length of the trees shadow) is about 7cm. 36.3m -7cm is 29.3m. 29.3m is about the height of the tree.
It will also cut down without hitting the greenhouse because the lawn was 31m and 14cm enough room for the tree to be cut down without trashing the greenhouse!

This is a good idea, Conor. Alexis from St Thomas Moore Roman Catholic School wrote:


The tree was 29.51 metres.
I worked this out because of the vital clue that when the bamboo stick stood at exactly one metre tall the shadow was 1.23 metres. Therefore, the shadow is 1.23 times as tall as the real height.
Taking this into account we can divide the height of the shadow of the tree by 1.23 to get the real height.

Maria who goes to IES in Spain, used this method too. She said:

As 1 m of cane produce a shadow of 1,23 m, X m of tree must produce a shadow of 36,3 m.
X= 363000 x 100/123=2951.2 cm is the height of the tree.
So the tree won´t reach the greenhouse!

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