Question

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Answer 1

Both equal sides have a length of 29 cm.

The third inequal side is 9 cm.

Explanation:

System of Equations

With the data provided in the problem, we can form a system of two equations with two unknowns.

Let's call x to each equal side of the isosceles triangle and y to the other side. One condition states that each equal side is 2 cm more than three times the other side. It can be written as:

`x=3y+2`

We also know the perimeter of the triangle is 67 cm. Since we have to equal sides to x:

`x+x+y=67`

`2x+y=67`

Let's put together both equations:

`x=3y+2`

`2x+y=67`

To solve the system, we can use the x from the first equation and replace it into the second equation:

`2(3y+2)+y=67`

Operating:

`6y+4+y=67`

Joining like terms:

`7y=67-4=63`

Solving for y:

`y=63/7=9`

The third inequal side is 9 cm. Now find the value of x.

`x=3y+2=3(9)+2=27+2=29`

Both equal sides have a length of 29 cm.