Legs 8 cm and 15 cm
- c² = 8² + 15² = 64 + 225 = 289.
- c = √289 = 17 cm.
- 17 is longer than 15 and 8.
Find the hypotenuse
Add the leg-square areas, then recover a length.
Write the relationship before substituting
Identify the hypotenuse, add the leg squares and take the nonnegative square root.
When both legs are known, use c = √(a² + b²). Label the hypotenuse as c, square each leg, add the areas and take the principal square root. Keep the squared sum together inside the radical. A side length must be positive for a non-degenerate triangle.
Explore the relationship
Predict first. Change one value, then explain the result. Diagrams show the entered dimensions; displayed decimals are rounded.
Check that the result is the longest side
For legs 9 m and 12 m, c² = 81 + 144 = 225 and c = 15 m. The result is larger than both legs and smaller than their sum, 21 m. These checks catch errors such as reporting 225 m as a length or adding the roots separately.
Keep exact and rounded forms connected
For legs 5 and 7, c = √74 exactly. This is approximately 8.6 to the nearest tenth. Keep √74 or the full calculator value for later calculations rather than using 8.6 prematurely. State units and the requested precision with the answer.
Worked examples
A rectangle is 6 m by 7 m. Find its diagonal.
- The adjacent rectangle sides meet at 90°, forming two legs.
- d = √(6² + 7²) = √85 ≈ 9.2 m to the nearest tenth.
- The diagonal is the hypotenuse of that right triangle.
Guided Practice
Find the hypotenuse for legs 7 m and 24 m.
A first hint
Square each leg before adding.
Compare your reasoning
c = √(49 + 576) = √625 = 25 m.
Practice
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
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Connections
Explain why a right triangle with legs 10 and 10 has hypotenuse 10√2, rather than 20. Give a decimal estimate as a check.
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