Understanding Pythagorean Relationships: Knowing When to Add or Subtract for 12-Year-Olds

Q: so will it be plus or minus

Short answer for a 12-year-old: use addition to find the hypotenuse, and use subtraction to find a missing leg. Important: when you solve for a side, you take the positive square root (lengths aren’t negative). If you know the two legs a and b and want the hypotenuse c: c = sqrt(a^2 + b^2) (you add the squares). If you know the hypotenuse c and one leg a and want the other leg b: b = sqrt(c^2 - a^2) (you subtract the square of the known leg from the hypotenuse square). Examples: 3-4-5 triangle: c = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. If c = 10 and a = 6: b = sqrt(10^2 - 6^2) = sqrt(100 - 36) = sqrt(64) = 8. Tip: You can rearrange c^2 = a^2 + b^2 to solve for any missing side (e.g., a^2 = c^2 - b^2). Want another practice problem?

Q: if b was missing

If b is missing, you know a and c (the hypotenuse). Use the rearranged formula b^2 = c^2 − a^2, so b = sqrt(c^2 − a^2). Make sure c is the longest side; if c^2 − a^2 is negative, those numbers can't form a right triangle. Examples: with a = 3 and c = 5, b^2 = 25 − 9 = 16, so b = 4. With a = 6 and c = 10, b^2 = 100 − 36 = 64, so b = 8. If a = 5 and c = 7, b^2 = 49 − 25 = 24, so b = sqrt(24) ≈ 4.90. Quick tip: always take the positive root since side length is positive. Try another: a = 8, c = 10 → b = sqrt(100 − 64) = sqrt(36) = 6.

Question

Understanding Pythagorean Relationships: Knowing When to Add or Subtract for 12-Year-Olds

Learning Corner · Accepted Answer

The Pythagorean Theorem helps us understand the relationship between the sides of a right triangle. The formula is a² + b² = c², where c is the hypotenuse (the longest side) and a and b are the other two sides.

To decide when to add or subtract, let's break it down:

Identifying the Hypotenuse: If you know two side lengths and need to find the hypotenuse, you'll use addition. For example, if you have sides of 3 and 4, you'd calculate:
  a² + b² = c²: For 3 and 4, that means 3² + 4² = c² → 9 + 16 = c² → 25 = c² → c = 5. Here, we added 9 and 16.

Working with the Hypotenuse: If you know the hypotenuse and one side, you subtract to find the other side. For example, if you know the hypotenuse is 5 and one side is 4:
  c² = a² + b²: This time, we rearrange it to find the other side: 5² = 4² + b² → 25 = 16 + b².
  Now, subtract 16 from both sides: 25 - 16 = b² → 9 = b² → b = 3. Here, we subtracted.

In summary, remember:

**Add** when finding the hypotenuse using two sides.
  **Subtract** when finding one side using the hypotenuse and the other side.

Practice with different triangles to get used to knowing when to add or subtract!

Understanding Pythagorean Relationships: Knowing When to Add or Subtract for 12-Year-Olds

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so will it be plus or minus

if b was missing