Question

Find x step by step ​

Answer 1

x = 11 cm

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

`(AD)/(AB)=(12)/(16)`

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

`(x+1)/(x+5)=(3)/(4)`

"Cross multiply" to get

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

Answer 2

`(4 + (x + 1))/(x + 1) = (16)/(12) \\ \\ (5 + x)/(x + 1) = (16)/(12) \\ \\ 12(5 + x) = 16(x + 1) \\ 60 + 12x = 16x + 16 \\ 4x = 44 \\ x = 11`