Chapter 12.9, Problem 1P

Jessica says she doesn‘t understand the Pythagorean theorem. She put numbers in for a, b, and c in the equation $a^2+b^2=c^2$ , but the equation isn't always true. For example, when she put in a = 2, b = 3, and c = 4, she got 4 + 9 = 16, which isn’t correct. Jessica wants to know why the Pythagorean theorem isn’t working‘ Write an informative paragraph discussing Jessica’s conundrum. Why does the Pythagorean theorem appear not to be correct? What misunderstanding does Jessica have?

To determine

The reason why the Pythagorean theorem is not satisfied for the given values.

Answer to Problem 1P

The Pythagorean theorem is applicable on right angled triangles only.

Explanation of Solution

Given Information:

Pythagorean theorem

  $a^2+b^2=c^2$

  $\begin{array}{l}a=2\\ b=3\\ c=4\end{array}$

Formula used

  $a^2+b^2=c^2$

Calculation:

According to J, the Pythagorean theorem is

  $a^2+b^2=c^2$

Where a, b, c = sides of a triangle.

J does not remember the fact that the Pythagorean theorem is only applicable on right angled triangles.

The reason why the theorem appears wrong to her is that the theorem cannot be applied for the triangle with arbitrary sides. According to Pythagorean theorem,

‘The sum of squares of sides of right angled triangle is equal to the square of hypotenuse.’