explain pythagorus theorem with example!
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Step-by-Step Solution
Step 1: State the Pythagorean Theorem
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Here, a and b are the lengths of the legs, and c is the length of the hypotenuse.
Step 2: Identify the sides of the right-angled triangle
Let's consider a right-angled triangle where the lengths of the two shorter sides (legs) are a=3 units and b=4 units. We need to find the length of the hypotenuse, c.
Step 3: Substitute values into the Pythagorean Theorem
Substitute the given values of a=3 and b=4 into the Pythagorean theorem equation.
Step 4: Calculate the squares of the sides
Calculate the square of each given side: 32=3×3=9 and 42=4×4=16.
Step 5: Sum the squares
Add the results from the previous step: 9+16=25.
Step 6: Solve for the hypotenuse
To find c, take the square root of both sides of the equation. Since length must be positive, we take the positive square root of 25, which is 5. Thus, the length of the hypotenuse is 5 units.