Question

the perimeter of the triangle shown on the right is 139 feet. find the length of each side. the length of the side that is represented by x is (simplify your answer. type an integer or a fraction.) the length of the side that is represented by 2x is (simplify your answer. type an integer or a fraction.) the length of the side that is represented by 8x - 4 is (simplify your answer. type an integer or a fraction.)

Explanation:

Step1: Set up perimeter equation

The perimeter of a triangle is the sum of its side - lengths. So, $x + 2x+(8x - 4)=139$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $(1 + 2+8)x-4=139$, which simplifies to $11x-4 = 139$.

Step3: Isolate the variable term

Add 4 to both sides of the equation: $11x-4 + 4=139 + 4$, resulting in $11x=143$.

Step4: Solve for x

Divide both sides by 11: $x=\frac{143}{11}=13$.

Step5: Find the length of each side

• For the side of length $x$, the length is $x = 13$.
• For the side of length $2x$, substitute $x = 13$: $2x=2\times13 = 26$.
• For the side of length $8x - 4$, substitute $x = 13$: $8x-4=8\times13-4=104 - 4=100$.

Answer:

The length of the side that is represented by $x$ is $13$.
The length of the side that is represented by $2x$ is $26$.
The length of the side that is represented by $8x - 4$ is $100$.