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The Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse: [tex]\( a^2 + b^2 = c^2 \)[/tex].



Answer :

GinnyAnswer
Sure! Let's walk through the application of the Pythagorean theorem step-by-step, using the values given.

### Step 1: Identify the lengths of the legs

We are given:
- One leg [tex]\(a\)[/tex] of the triangle is 3 units.
- The other leg [tex]\(b\)[/tex] of the triangle is 4 units.

### Step 2: Calculate the squares of each leg

First, we calculate the square of leg [tex]\(a\)[/tex]:
[tex]\[ a^2 = 3^2 = 9 \][/tex]

Next, we calculate the square of leg [tex]\(b\)[/tex]:
[tex]\[ b^2 = 4^2 = 16 \][/tex]

### Step 3: Sum the squares of the legs

Now, we sum the squares of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[ a^2 + b^2 = 9 + 16 = 25 \][/tex]

### Step 4: Calculate the square root to find the hypotenuse

Finally, to find the length of the hypotenuse [tex]\(c\)[/tex], we take the square root of the sum:
[tex]\[ c = \sqrt{25} = 5.0 \][/tex]

### Summary of the results

- [tex]\(a^2 = 9\)[/tex]
- [tex]\(b^2 = 16\)[/tex]
- [tex]\(a^2 + b^2 = 25\)[/tex]
- [tex]\(c = 5.0\)[/tex]

Thus, for a right triangle with legs [tex]\(a = 3\)[/tex] and [tex]\(b = 4\)[/tex], the hypotenuse [tex]\(c\)[/tex] is 5.0 units.

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