Chapter 8, Problem 3SGR

To determine

Whether each sentence is true or false.

Answer to Problem 3SGR

The given sentence is false.

To find the length of the hypotenuse of a right triangle, take the square root of the sum of the squares of the legs.

Explanation of Solution

Given:

The given sentence is:

To find the length of the hypotenuse of a right triangle, take the square root of the difference of the squares of the legs.

Calculation:

According to the Pythagoras Theorem, the square of the length of hypotenuse in a right-angled triangle is equal to the sum of the squares of the lengths of legs.

Consider the right triangle below:

  

Here, the lengths of the legs are 3 and 4 and the hypotenuse is x.

The value of x can be calculated as:

  $\begin{array}{l}x=\sqrt{3^2+4^2}\\ x=\sqrt{9+16}\\ x=\sqrt{25}\\ x=5\end{array}$

Hence, the given sentence is false.

To find the length of the hypotenuse of a right triangle, take the square root of the sum of the squares of the legs.