Question

determine the perimeter of the given triangle. write your answer in the simplest form. the triangle has sides: 2.8x - 3, 2.8x - 3, 1.2x + 4

Explanation:

Step1: Identify the triangle type

The triangle has two sides with length \(2.8x - 3\), so it's isosceles. Thus, the equal sides imply \(2.8x - 3=1.2x + 4\).

Step2: Solve for \(x\)

Subtract \(1.2x\) from both sides: \(2.8x - 1.2x- 3=4\) → \(1.6x - 3 = 4\).
Add 3 to both sides: \(1.6x=4 + 3\) → \(1.6x = 7\).
Divide by 1.6: \(x=\frac{7}{1.6}=\frac{35}{8}=4.375\).

Step3: Calculate perimeter

Perimeter \(P=(2.8x - 3)+(2.8x - 3)+(1.2x + 4)\).
Combine like terms: \(P=(2.8x+2.8x+1.2x)+(-3-3 + 4)\) → \(P = 6.8x-2\).
Substitute \(x = 4.375\): \(6.8\times4.375-2\).
\(6.8\times4.375 = 29.75\), so \(29.75-2 = 27.75\).

Answer:

The perimeter of the triangle is \(27.75\) (or if we keep \(x=\frac{35}{8}\), perimeter can also be expressed in terms of \(x\) or simplified fraction, but numerical value here is \(27.75\)).