Question

riding find the length of the hypotenuse of the right triangle use pencil and paper explain how you can interpret the Pythagorean theoremusing the areas of squares

Answer 1

Question 1:

- Use of the area of squares to explain the Pythagoras theorem is given below

- The 3 squares given above have dimensions: a, b, and c.

- The areas of the squares are given by:

`\begin{gathered} \text{For square of length }a\to a^2 \\ \text{For square of length }b\to b^2 \\ \text{For square of length }c\to c^2 \end{gathered}`

- The Pythagoras theorem states that:

"The sum of the areas of the smaller squares add up to the area of the biggest square"

Thus, we have:

`c^2=a^2+b^2`

Question 2:

- We can apply the theorem as follows:

`\begin{gathered} 10^2+24^2=c^2 \\ 100+576=c^2 \\ 676=c^2 \\ \text{Take square root of both sides} \\ \\ c=\sqrt[]{676} \\ c=26 \end{gathered}`

Thus, the value of c is 26