A cuboid has a diagonal of length 9cm and a square base of side 4cm. What is its height?
9cm
\(\sqrt{65}\)cm
\(4\sqrt{2}\)cm
7cm
6.5cm
Explanation
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Discussions (3)
The answer is supposed to be D, 7cm, since the cuboid has base of 4cm, the diagonal of the base will be 4√2cm, and from there, we will use it to get the height
I.e
x² + (4√2)² = 9²
x² + 32 = 81
x² = 49
x = 7cm
Or we could just use the formula
d² = a² + b² + h²
Where a and b are the length and width of the base, h is the height and d is the diagonal
=> 9² = 4² + 4² + h²
When you solve, you'll get h = 7cm.
The answer is supposed to be D. The diagonal serves as the Hypotenuse of the right angled triangle. The base of the triangle can be found using pythagoras theorem which gives us 4 root 2. We can then find the height which gives us 7cm.
