Questions: Find an expression, in its simplest form, for the perimeter of this pentagon. Find the value of s if the perimeter of the pentagon is equal to 42 units.

Find an expression, in its simplest form, for the perimeter of this pentagon.

Add all sides

The perimeter of the pentagon is the sum of all its sides: Perimeter = \((2s + 2) + (s + 3) + (2s + 2) + s + s\)

Combine like terms

Perimeter = \(2s + 2 + s + 3 + 2s + 2 + s + s\) Perimeter = \(7s + 7\)

\(\boxed{7s+7}\)

Find the value of \(s\) if the perimeter of the pentagon is equal to 42 units.

Set up the equation

The perimeter is given as 42 units. We have the expression for the perimeter as \(7s + 7\). So we can set up the equation: \(7s + 7 = 42\)

Subtract 7 from both sides

Subtract 7 from both sides of the equation: \(7s + 7 - 7 = 42 - 7\) \(7s = 35\)

Divide both sides by 7

Divide both sides by 7: \(\frac{7s}{7} = \frac{35}{7}\) \(s = 5\)

\(\boxed{s=5}\)

Perimeter of the pentagon: \(7s + 7\) Value of \(s\): \(s = 5\)