Question

Using the Pythagorean Theorem, calculate the hypotenuse of a right triangle if the sides of the legs are 12 cm and 16 cm?

Answer 1

Answer:

20 cm

Step-by-step explanation:

The pythagorean theorem states

a^2 + b^2 = c^2

where a and b are the legs and c is the hypotenuse

12^2 + 16^2 = c^2

144+256 = c^2

400 = c^2

Take the square root of each side

sqrt(400) = sqrt(c^2)

20 = c

Answer 2

Your answer is 20cm.

The Pythagorean Theorem is a² + b² = c², which means that to find the length of the hypotenuse (which is represented by the letter c in this equation), we need to square both side lengths and add them together, and then squareroot the result.

This gives us:

a² + b² = c²

(12)² + (16)² = c²

144 + 256 = c²

400 = c²

20 = c

If you are unable to use a calculator for this question, you could also spot that this is a good example of a 3-4-5 triangle, which is a right-angled triangle where the two legs have length 3 and 4, and the hypotenuse has a length of 5. We can spot this because dividing 12 and 16 by 4 gets us 3 and 4, and 20 divided by 4 is 5.

I hope this helps! Let me know if you have any questions :)