Respuesta :

Answer:

[tex] \frac{4 + (x + 1)}{x + 1} = \frac{16}{12} \\ \\ \frac{5 + x}{x + 1} = \frac{16}{12} \\ \\ 12(5 + x) = 16(x + 1) \\ 60 + 12x = 16x + 16 \\ 4x = 44 \\ x = 11[/tex]

ivycoveredwalls

Answer:

x = 11 cm

Step-by-step explanation:

Segments DE and BC are parallel (that's what the arrows tell you), so there are two similar triangles formed.

[tex]\triangle{ADE} \sim \triangle{ABC}[/tex]

Corresponding sides are in proportion, so

[tex]\frac{AD}{AB}=\frac{12}{16}[/tex]

The length of AB is (x + 1) + 4 = x + 5, and 12/16 simplifies to 3/4, so

[tex]\frac{x+1}{x+5}=\frac{3}{4}[/tex]

"Cross multiply" to get

[tex]4(x+1)=3(x+5)\\4x+4=3x+15\\4x=3x+11\\x=11[/tex]

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