sides of a triangle

Question

The perimeter of a triangle is 82 feet. One side of the triangle is 2 times the second side. The third side is 2 feet longer than the second side. Find the length of each side.

Answer 1

Step 1: Consider the second side of the triangle to be x.

Step 2: Find an expression for the first side. The first side is 2 times the second side.

So, 2x

Step 3: Find an expression for the third side. The third side is 2 feet longer than the second side.

So, x+2

Step 4: Create an equation to show that all the sides added up equals the perimeter of the triangle.

(x)+(2x)+(x+2) = 82

Step 5: Solve for x or the second side.

x+2x+x+2 = 82

4x+2 = 82

-2 -2

---------------

4x = 80

---- ----

4 4

x = 20

Second side = 20 feet

Step 6: Solve for the first side by replacing the value of x into the expression 2x.

First side = 2x

= 2(20)

= 40

First side = 40 feet

Step 7: Find the third side by plugging in the value of x into the expression x+2.

Third side = x+2

= 20+2

= 22

Third side = 22 feet

Answer 2

The perimeter is going to be equal to the sum of the lengths of the 3 sides of the triangle.

Also, the problem discusses 2 sides in relation to the second side. Let's set the second side length to be equal to x.

That means the one side that is 2 times the second side will be equal to: 2x

The third side that is 2 feet longer than the second side will be equal to: x+2

The sum of the 3 sides will now be: x + 2x + x+2

Since the perimeter is 82 we can set this equal to our equation and solve for x.

82 = x + 2x + x + 2

Combine like terms and subtract both sides by 2.

80 = 4x

Divide both sides by 4.

x = 20 ft.

This means that our second side is 20 feet.

Our first side is 2x so it is equal to 2(20) = 40 feet

Our third side is x+2 so it is equal to 20 + 2 = 22 feet.

Our 3 sides of our triangle are: 20, 22, and 40 feet FINAL ANSWER