Question

The length of the hypotenuse of a right triangle is $\sqrt{3}$ m.Lengths of other two sides are 1 m and $\sqrt{2}$ m respectively. To approximate the value of the new number $\sqrt{3}$, we need to select the numbers and square them to see if its equal to 3.which of the following is the range of numbers we can select?

• A. $\sqrt{2}$ >hypotenuse > $\sqrt{2}+1$
• B. $\sqrt{2}$ <hypotenuse < $\sqrt{2}+1$
• C. $\sqrt{1}$ <hypotenuse < $\sqrt{2}+1$
• D. $\sqrt{2}$ <hypotenuse < $\sqrt{5}+1$

Answer 1

The correct option is B

$\sqrt{2}$ <hypotenuse < $\sqrt{2}+1$

Since the sum of the lengths of any two sides of a triangle must be greater than the length of the third side,

The length of the hypotenuse must be between $\sqrt{2}$ and $\sqrt{2}+1$