Answer:
The perimeter is [tex]32\sqrt{7}[/tex] cm.
Step-by-step explanation:
Perimeter is found by adding all sides of the triangle together. So, this is what we need to find: [tex]8\sqrt{7}+4\sqrt{63}+6\sqrt{28}[/tex]
- Only like radicals can be added or subtracted from one another. They'll have the same root number (which seems to be true for this question) as well as the radicand, which is the number/expression under the radical.
Look at the number under the radical: 7, 63, and 28. These numbers all share a factor of 7: 7/7 = 1, 63/7 = 9, 28/7 = 4.
Notice how 9 and 4 are perfect squares, so we can simplify the radicals using this common factor of 7.
[tex]8\sqrt{7}[/tex] remains the same; [tex]4\sqrt{63}=4\sqrt{9(7)} =4(3)\sqrt{7}=12\sqrt{7}[/tex]; and
[tex]6\sqrt{28}=6\sqrt{4(7)}=6(2)\sqrt{7}=12\sqrt{7}[/tex]. Now they are like radicals and can be added!
[tex]8\sqrt{7}+12\sqrt{7}+12\sqrt{7}=32\sqrt{7}[/tex]
