Q41. - Algebra 2

Question

MATH HISTORY

Use the following information.

The Greek mathematician Pythagoras believed that all things could be described by numbers. By “number” he meant positive integers.

41. Use the formula $c=\sqrt{2s^2}$ to calculate the length of the hypotenuse c, or the longest side, of this right triangle using s, the length of one leg.

Step-by-Step Solution

Answer

The length of the hypotenuse is $c=\sqrt{2}$ units

Step 1 - Observe from image

From given image length of one leg of right triangle is 1 unit

Step 2 - Substitution

Substitute 1 for $s$ in given formula

$c=\sqrt{2{\left(1\right)}^2}$

Step 3 - Simplify 2 1 2

To evaluate the length of hypotenuse, first evaluate power then perform multiplication and finally simplify square root as shown below.

$\begin{array}{c}c=\sqrt{2{\left(1\right)}^2}\\ =\sqrt{2\left(1\right)}\\ =\sqrt{2}\end{array}$

As $\sqrt{2}$ lies between whole number 1 and 2 so it cannot be simplified further.