The first side of a triangle is twice the second, and the third is 20 feet less than three times the second. the perimeter is 106 feet. find the three sides.
Accepted Solution
A:
Let's use 'x' for the first side, 'y' for the second, and 'z' for the third. Translate the statements into equations:
"The first side of a triangle is twice the second" x = 2y
"the third is 20 feet less than three times the second" z = 3y - 20
"the perimeter is 106 feet" x + y + z = 106
Now let's plug in what 'x' and 'z' equal in the first two equations into the last equation:
2y + y + 3y - 20 = 106
Combine like terms(2y + y + 3y = 6y):
6y - 20 = 106
Add 20 to both sides:
6y = 126
Divide 6 to both sides:
y = 21
So the length of the second side is 21 feet. We can plug this into the first two equations to find the lengths of the other sides: