Question

midterm review score: 22.99/100 answered: 5/18 question 6 consider the triangle shown on the picture. find all three sides of the triangle above, given that the perimeter of the triangle is 67 unit. separate your answers with commas in the answer box below.

Explanation:

Step1: Set up perimeter equation

The perimeter of a triangle is the sum of its sides. So, $(6x - 3)+(4x + 7)+(5x+3)=67$.
Combining like - terms, we get $(6x+4x + 5x)+(-3 + 7+3)=67$, which simplifies to $15x + 7=67$.

Step2: Solve for x

Subtract 7 from both sides of the equation: $15x+7 - 7=67 - 7$, so $15x=60$.
Divide both sides by 15: $\frac{15x}{15}=\frac{60}{15}$, and $x = 4$.

Step3: Find the lengths of the sides

For the first side: Substitute $x = 4$ into $6x-3$, we get $6\times4-3=24 - 3=21$.
For the second side: Substitute $x = 4$ into $4x + 7$, we get $4\times4+7=16 + 7=23$.
For the third side: Substitute $x = 4$ into $5x+3$, we get $5\times4+3=20 + 3=23$.

Answer:

21,23,23