Question

7 simplify an expression for the perimeter of the equilateral triangle shown below. 1.75x - 2

Explanation:

Step1: Recall the formula for the perimeter of an equilateral triangle

An equilateral triangle has all three sides equal. The perimeter \(P\) of a triangle is the sum of its side lengths. For an equilateral triangle with side length \(s\), \(P = 3s\). Here, \(s=1.75x - 2\).

Step2: Substitute the side - length into the perimeter formula

Substitute \(s = 1.75x-2\) into \(P = 3s\). We get \(P=3(1.75x - 2)\).

Step3: Apply the distributive property

Using the distributive property \(a(b + c)=ab+ac\) (here \(a = 3\), \(b = 1.75x\), \(c=-2\)), we have \(P=3\times1.75x-3\times2\).
Since \(3\times1.75x = 5.25x\) and \(3\times2 = 6\), the expression for the perimeter is \(P = 5.25x-6\).

Answer:

\(5.25x - 6\)