Question

solving problems with equations:
ex. 2 - examine the pentagon.
(image of a pentagon with sides labeled 3x, x - 4, 5x, 8x, 7x)
a) find a simplified expression for the perimeter of the following, in terms of x.
b) use your expression to find the perimeter when x = 5

Explanation:

Part (a)

Step1: Recall perimeter definition

Perimeter of a polygon is the sum of all its side lengths. The pentagon has sides \(3x\), \(x - 4\), \(5x\), \(8x\), and \(7x\). So we need to add these expressions: \(P=(3x)+(x - 4)+(5x)+(8x)+(7x)\).

Step2: Combine like terms

First, combine the \(x\)-terms: \(3x+x + 5x+8x+7x=(3 + 1+5 + 8+7)x=24x\). Then we have the constant term \(-4\). So the simplified expression is \(24x-4\).

Step1: Substitute \(x = 5\) into the perimeter formula

We found the perimeter formula in part (a) is \(P = 24x-4\). Now substitute \(x = 5\) into this formula: \(P=24(5)-4\).

Step2: Calculate the value

First, calculate \(24\times5 = 120\). Then subtract 4: \(120-4 = 116\).

Answer:

The simplified expression for the perimeter is \(\boldsymbol{24x - 4}\).

Part (b)