#10
Top 50 Mistake
Adding when finding a shorter side
"The Plus-Minus Mixup"
The Mistake in Action
A right-angled triangle has hypotenuse 13cm and one side 5cm. Find the other side.
Wrong: $a^2 = 13^2 + 5^2 = 194$ $a = 13.9$ cm
Why It Happens
Students always add the squares without thinking about which side they're finding.
The Fix
Finding hypotenuse: ADD the squares of the shorter sides Finding shorter side: SUBTRACT (hypotenuse² - known side²)
$$a^2 = c^2 - b^2$$ $$a^2 = 13^2 - 5^2 = 169 - 25 = 144$$ $$a = \sqrt{144} = 12\text{cm}$$
Check: Is 12cm < 13cm (the hypotenuse)? Yes! ✓
Spot the Mistake
Can you identify where this student went wrong?
Hypotenuse = 13cm, one side = 5cm. Find the other side.
$a^2 = 13^2 + 5^2$
$a^2 = 194$
$a = 13.9$ cm
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: