Question

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Answer 1

Answer:

Both equal sides have a length of 29 cm.

The third inequal side is 9 cm.

Step-by-step 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.