Question

geometry chapter 1 individual test version a
please show all work neatly and clearly on this test.

1. a) suppose the three sides of △abc are ab = x + 2 cm, bc = 2x + 2 cm, and ac = 3x - 1 cm. using the fact that the perimeter of the triangle is 33 cm, write an equation and solve for x.

b) using your solution from part (a), what are the lengths of the sides of the triangle? show work.
name: callum white
score: /100

Explanation:

Step1: Set up perimeter equation

The perimeter of a triangle is the sum of its sides. So, $AB + BC+AC = 33$. Substituting the given expressions for the sides, we get $(x + 2)+(2x + 2)+(3x-1)=33$.

Step2: Combine like - terms

Combining the $x$ terms and the constant terms on the left - hand side: $(x+2x + 3x)+(2 + 2-1)=33$, which simplifies to $6x+3 = 33$.

Step3: Isolate the variable term

Subtract 3 from both sides of the equation: $6x+3 - 3=33 - 3$, resulting in $6x=30$.

Step4: Solve for x

Divide both sides by 6: $\frac{6x}{6}=\frac{30}{6}$, so $x = 5$.

Step5: Find the side lengths

• For $AB=x + 2$, substituting $x = 5$, we get $AB=5 + 2=7$ cm.
• For $BC=2x + 2$, substituting $x = 5$, we get $BC=2\times5+2=10 + 2=12$ cm.
• For $AC=3x-1$, substituting $x = 5$, we get $AC=3\times5-1=15 - 1=14$ cm.

Answer:

$AB = 7$ cm, $BC = 12$ cm, $AC = 14$ cm