Question

The three sides of a triangle are n, 4n - 2, and 4n - 7. If the perimeter of the triangle is 45 cm, what is the length of each side? Separate multiple entries with a comma.

Answer 1

Perimeter of a triangle and equations

6, 22, 17

Step-by-step explanation

Step 1: writing the equation

We have a triangle with sides n, 4n - 2, and 4n - 7

We obtain its perimeter if we add all its sides:

n + 4n - 2 + 4n - 7

Since the perimeter is 45 cm, then:

n + 4n - 2 + 4n - 7 = 45

combining like terms:

n + 4n +4n = 9n

and

-2 - 7 = -9

then, we have:

n + 4n - 2 + 4n - 7 = 45

↓

9n - 9 = 45

Step 2: finding n

Now we solve the equation:

9n - 9 = 45

↓ taking -9 to the right

9n - 9 + 9 = 45 + 9

9n = 54

↓ taking 9 to the right

n = 54/9 = 6

Then, n = 6

Step 3: sides measure

Since the measure of the first side is given by n,

then its length is

n = 6

SInce the measure of the second side is given by 4n-2,

then its length is

4n - 2 = 4 · 6 - 2

= 24 - 2

= 22

SInce the measure of the third side is given by 4n - 7,

then its length is

4n - 7 = 4 ·6 - 7

= 24 - 7

= 17

That is why the measures are 6, 22 and 17.