Answer:
width = 40 cm
Step-by-step explanation:
Since the pentagons are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{4x}{x}[/tex] = [tex]\frac{48}{x+2}[/tex] ( cross- multiply )
4x(x + 2) = 48x ← distribute left side
4x² + 8x = 48x ( subtract 48x from both sides )
4x² - 40x = 0 ← factor out 4x from each term on left side
4x(x - 10) = 0
Equate each factor to zero and solve for x
4x = 0 ⇒ x = 0
x - 10 = 0 ⇒ x = 10
However, x > 0 then x = 10
Thus width = 4x = 4 × 10 = 40 cm
