1. The problem is to find the length $x$ of the hypotenuse in each right triangle given the legs. 2. We use the Pythagorean theorem: $$x = \sqrt{a^2 + b^2}$$ where $a$ and $b$ are the legs of the right triangle. 3. Calculate each $x$: - Top-left: $a=6$, $b=3$ $$x = \sqrt{6^2 + 3^2} = \sqrt{36 + 9} = \sqrt{45} = 6.7$$ cm - Top-center: $a=6$, $b=3$ Same as above, $x=6.7$ cm - Top-right: $a=4.4$, $b=6.6$ $$x = \sqrt{4.4^2 + 6.6^2} = \sqrt{19.36 + 43.56} = \sqrt{62.92} = 7.9$$ cm - Bottom-left: $a=7$, $b=4$ $$x = \sqrt{7^2 + 4^2} = \sqrt{49 + 16} = \sqrt{65} = 8.1$$ cm - Bottom-center: $a=3.4$, $b=6.6$ $$x = \sqrt{3.4^2 + 6.6^2} = \sqrt{11.56 + 43.56} = \sqrt{55.12} = 7.4$$ cm - Bottom-right: $a=7.5$, $b=6.1$ $$x = \sqrt{7.5^2 + 6.1^2} = \sqrt{56.25 + 37.21} = \sqrt{93.46} = 9.7$$ cm 4. Final answers rounded to 1 decimal place: - Top-left: $6.7$ cm - Top-center: $6.7$ cm - Top-right: $7.9$ cm - Bottom-left: $8.1$ cm - Bottom-center: $7.4$ cm - Bottom-right: $9.7$ cm