Question

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.

Answer 1

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:

x = 2y

x = 2(21)

Multiply:

x = 42

So the length of the first side is 42 feet.

z = 3y - 20

z = 3(21) - 20

Multiply:

z = 63 - 20

Subtract:

z = 43

So the length of the third side is 43 feet.