Q 7. - Calculus

Question

State the Pythagorean theorem and give an example of a triangle that illustrates the theorem. 

Step-by-Step Solution

Answer

The Pythagorean theorem states that if a right triangle has legs of lengths $a$ and $b$ and hypotenuse of length $c$, then $a^2+b^2=c^2$.

For example a triangle having sides $4$ units, $3$ unist and $5$ units

$$\begin{gathered} \Rightarrow 5^2=4^2+3^2 \\ \Rightarrow 25=25 \end{gathered}$$

Step 1. Definition of Pythagorean theorem

The Pythagorean theorem states that if a right triangle has legs of lengths $a$ and $b$ and hypotenuse of length $c$, then $a^2+b^2=c^2$.

Step 2. Example with explanation

Let us suppose we have a triangle with length $3$ units, $4$ units and $5$ units.

So we know that the hypotenuous is always bigger than other two.

Therefore, According to pythagorean theorem $5^2=4^2+3^2$

$\Rightarrow 25=16+9$

$\Rightarrow 25=25$ [Hence proved]