SME
Grade 8 Math · Geometry
Pythagorean theorem and distance between points
Use this for “A right triangle has legs of 3 cm and 4 cm. How long is the hypotenuse?”
Diagram
a² + b² = c²
3² + 4² = 9 + 16 = 25
c = √25 = 5 cm
This is an example. Type your own values to start a new problem.
a
2
+
b
2
=
c
2
Formulas
a
2
+
b
2
=
c
2
(leg
a²
+
leg
b²
=
hypotenuse²)
3
2
+
4
2
=
5
2
Assumptions
•
The triangle has a right angle between the legs a and b; c is the hypotenuse, the longest side.
•
The square on each side has area side²; the two smaller squares together cover the biggest one.
•
To find a leg, take the other leg’s square from the hypotenuse’s square.
•
All three sides use the same unit.
Step-by-step
WE KNOW
a = 3 cm (leg a), b = 4 cm (leg b)
FIND
hypotenuse (c)
Step 1 · Find hypotenuse (c)
Use a² + b² = c² (leg a² + leg b² = hypotenuse²)
Square each leg, add them, then take the square root.
3
2
+
4
2
=
c
2
c
=
√
3
2
+
4
2
c
=
√
9 + 16
c
=
√
25
c
=
5
cm
Check
Put the numbers back in. Both sides should match.
3
2
+
4
2
=
5
2
✓
Topic check
See what you know: 5 questions on this topic
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More problem types
Distance between two points
Use this for “Find the distance between (−9, −12) and (0, 0)” or “How long is the segment on the grid?”
A diagonal through a box
Use this for “Will a 30 cm umbrella fit flat in a 20 cm by 15 cm by 18 cm box, corner to corner?”
Is it a right triangle?
Use this for “Which of these could be the sides of a right triangle?” with the converse of the Pythagorean theorem.