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For any right triangle, the side lengths of the triangle can be put in the equation a2 + b2 = c2 where a, b, and c are the side lengths. A triangle with the side lengths 3 inches, 4 inches, and 5 inches is a right triangle. Which way(s) can you substitute the values into the equation to make it true? Which variable has to match the longest side length? Why?

Sagot :

Mhanifaidn

Step-by-step explanation:

Given relationship is the Pythagorean theorem.

a and b are legs, c is the hypotenuse. The hypotenuse is the greatest side of the right triangle. The square of the hypotenuse is equal to the sum of the squares of the other sides.

We can substitute side measures in two ways:

  • a = 3, b = 4, c = 5

or

  • a = 4, b = 3, c = 5

The variable c has a fixed position so we can't have more than two ways.

First of all lets look at the sides and then write it in two different ways:

  • 3 inches
  • 4 inches
  • 5 inches

*Note that:- When writing two different ways, the value of c will not change because it is the hypotenuse and the hypotenuse is always the longest side.

  • We can interchange the values of perpendicular and base since they do not affect the final answer.
  • The largest number is always the hypotenuse and cannot be changed.

Now, Two different ways of writing the side lengths:

[tex] \mathbb{C^{2} =A^{2} +B^{2} }[/tex]

  • A = 3, B = 4, C = 5
  • A = 4, B = 3, C = 5
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