Question

Find x step by step ​

Answer 1

Answer:

$\frac{4 + (x + 1)}{x + 1} = \frac{16}{12} \\ \\ \frac{5 + x}{x + 1} = \frac{16}{12} \\ \\ 12(5 + x) = 16(x + 1) \\ 60 + 12x = 16x + 16 \\ 4x = 44 \\ x = 11$

Answer 2

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.

$\triangle{ADE} \sim \triangle{ABC}$

Corresponding sides are in proportion, so

$\frac{AD}{AB}=\frac{12}{16}$

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

$\frac{x+1}{x+5}=\frac{3}{4}$

"Cross multiply" to get

$4(x+1)=3(x+5)\\4x+4=3x+15\\4x=3x+11\\x=11$