The height of a triangle is given as \( \sqrt{45} \). Between which two integers is the height of the triangle? 0.2 and 3 3 and 4 0.6 and 7 0.7 and 8

To determine between which two integers the height of the triangle, given as \( \sqrt{45} \), lies, we first need to calculate \( \sqrt{45} \). We can simplify \( \sqrt{45} \) as follows: \[ \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5} \] Next, we need to approximate \( \sqrt{5} \). We know that: \[ 2^2 = 4 \quad \text{and} \quad 3^2 = 9 \] This means \( 2 < \sqrt{5} < 3 \). A more precise approximation of \( \sqrt{5} \) is approximately \( 2.236 \). Now we can calculate \( 3\sqrt{5} \): \[ 3\sqrt{5} \approx 3 \times 2.236 = 6.708 \] Now we can determine between which two integers \( 6.708 \) lies. The integers surrounding \( 6.708 \) are \( 6 \) and \( 7 \). Thus, the height of the triangle \( \sqrt{45} \) lies between the integers \( 6 \) and \( 7 \). The correct answer is: **0.6 and 7**.