Finding the hypotenuse
Use Pythagoras' theorem to find the length of the hypotenuse in a right-angled triangle.
Worked examples
Find the hypotenuse — integer result
Straightforward
Problem
A right-angled triangle has legs of length cm and cm. Find the length of the hypotenuse.
1
Write Pythagoras' theorem.
2
Substitute the known leg lengths.
3
Take the square root to find .
Answer
The hypotenuse is cm.
Find the hypotenuse — decimal result
Moderate
Problem
A right-angled triangle has legs of length cm and cm. Find the length of the hypotenuse, rounded to 2 decimal places.
1
Write Pythagoras' theorem.
2
Substitute the known leg lengths.
3
Take the square root. The result is not a whole number, so round to 2 decimal places.
Answer
The hypotenuse is approximately cm.
Find the hypotenuse — multi-step problem
Challenging
Problem
A square has area cm². Find the length of its diagonal, rounded to 2 decimal places.
1
Find the side length of the square from its area.
2
The diagonal of a square divides it into two right-angled triangles, each with legs equal to the side length. Apply Pythagoras' theorem.
3
Take the square root and round to 2 decimal places.
Answer
The diagonal is approximately cm.
Practise
Q1·Straightforward
A right-angled triangle has legs of length cm and cm. Find the length of the hypotenuse.
Explanation
Q2·Straightforward
A right-angled triangle has legs of length cm and cm. Find the length of the hypotenuse.
Explanation
Q3·Straightforward
A right-angled triangle has legs of length cm and cm. Find the length of the hypotenuse.
Explanation
Q4·Straightforward
A right-angled triangle has legs of length cm and cm. Find the length of the hypotenuse.
Explanation
Q5·Moderate
A right-angled triangle has legs of length cm and cm. Find the length of the hypotenuse, rounded to 2 decimal places.
Explanation
Q6·Moderate
A right-angled triangle has legs of length cm and cm. Find the length of the hypotenuse, rounded to 2 decimal places.
Explanation
Q7·Moderate
A right-angled triangle has legs of length cm and cm. Find the length of the hypotenuse, rounded to 2 decimal places.
Explanation
Q8·Moderate
A right-angled triangle has legs of length cm and cm. Find the length of the hypotenuse, rounded to 2 decimal places.
Explanation
Q9·Challenging
A square has area cm². Find the length of its diagonal, rounded to 2 decimal places.
Explanation
Side length: cm.
Q10·Challenging
A rectangle has area cm² and length cm. Find the length of its diagonal, rounded to 2 decimal places.
Explanation
Width: cm.
Q11·Challenging
The area of a right-angled triangle is cm². The shorter leg is cm. Find the length of the hypotenuse.
Explanation
Longer leg: cm.
Q12·Challenging
A right-angled triangle has legs in the ratio . The shorter leg is cm. Find the length of the hypotenuse.
Explanation
Longer leg: cm.