Building Blocks
Can you find the length of AB in this diagram?
Age
14 to 16
Challenge level
Problem
Each of the cubes in the diagram have sides of length 3 cm.
Image
The length of AB is $\sqrt{k}$ cm.
What is the value of $k$?
Student Solutions
The shape in the diagram is 3 blocks (9cm) long, and it is 2 blocks (6cm) deep. So by Pythagoras, the "shadow of AB on the floor" has length $\sqrt{9^2+6^2} = \sqrt{117}$ cm, as shown in the diagram below.
Image
The figure is also 2 blocks (6cm) high, as shown below, so can now use Pythagoras again to find $AB$:
Image
$AB^2 = (\sqrt{k})^2 = (\sqrt{117})^2+6^2 = 117+36 = 153$
Therefore $k=153$