Answer:
1. [tex]6^2+8^2=10^2[/tex]
2. [tex]\[ (\sqrt{5})^2 + (\sqrt{3})^2 = (\sqrt{8})^2 \][/tex]
3. [tex]\[ 5^2 + (\sqrt{5})^2 = (\sqrt{30})^2 \][/tex]
4. [tex]\[ 1^2 +6^2= (\sqrt{37})^2[/tex]
5. [tex](\sqrt{2}~ )^2 ~+ (\sqrt{7} ~)^2 = 3^2[/tex]
Step-by-step explanation:
In a right triangle, the hypotenuse represents the largest side. The hypotenuse squared is the sum of the other two sides in the triangle squared. In order to find the expression for each answer option, find which term squared has the highest value and the two lowest values add up to equal that highest value.
[tex]\hrulefill[/tex]
[tex]1. ~10,6,8\\\\\text{Notice that \textbf{10} has the highest value, that means it will be the hypotenuse}\\\\\text{Therefore, the squares of the other two sides sum up to the hypotenuse squared.}\\\\\textbf{Answer: } \boxed{6^2+8^2=10^2}\\\hrulefill[/tex]
[tex]\rule{\linewidth}{0.4pt}[/tex]
[tex]2. ~\sqrt{5} , \sqrt{3} , \sqrt{8} \\\\\text{Notice that \textbf{root 8} has the highest value, that means it will be the hypotenuse}\\\\\text{Therefore, the squares of the other two sides sum up to the hypotenuse squared.}\\\\\textbf{Answer: } \boxed{(\sqrt{5})^2 + (\sqrt{3})^2 = (\sqrt{8})^2}\\\hrulefill[/tex]
[tex]\rule{\linewidth}{0.4pt}[/tex]
[tex]3. ~5 , \sqrt{5} , \sqrt{30} \\\\\text{Notice that \textbf{root 30} has the highest value, that means it will be the hypotenuse}\\\\\text{Therefore, the squares of the other two sides sum up to the hypotenuse squared.}\\\\\textbf{Answer: } \boxed{5^2 + (\sqrt{5})^2 = (\sqrt{30})^2}\\\hrulefill[/tex]
[tex]\rule{\linewidth}{0.4pt}[/tex]
[tex]4. ~1 , \sqrt{37} , 6 \\\\\text{Notice that \textbf{root 37} has the highest value, that means it will be the hypotenuse}\\\\\text{Therefore, the squares of the other two sides sum up to the hypotenuse squared.}\\\\\textbf{Answer: } \boxed{1^2 + 6^2 = (\sqrt{37})^2}\\\hrulefill[/tex]
[tex]\rule{\linewidth}{0.4pt}[/tex]
[tex]5. ~3 , \sqrt{2} , \sqrt{7} \\\\\text{Notice that \textbf{3} has the highest value, that means it will be the hypotenuse}\\\\\text{Therefore, the squares of the other two sides sum up to the hypotenuse squared.}\\\\\textbf{Answer: } \boxed{(\sqrt2)^2 + (\sqrt{7})^2 = 3}\\\hrulefill[/tex]
[tex]\rule{\linewidth}{0.4pt}[/tex]
Hope this helps!
