Question

Find the missing length of the following trapezoid

Answer 1

1) The length of
`DC` is 20.

2) The length of
`PS` is 17.

Explanation:

1) If
`DR = RE` and
`CS = SB`, then we can use the following proportionality ratio:

`(DE)/(DR) = (32 - x)/(26 - x)` (1)

Where
`x` is the length of segment
`\overline{CD}`.

If
`DE = 2\cdot DR`, then the value of
`x` is:

`2 = (32-x)/(26-x)`

`52 - 2\cdot x = 32 - x`

`20 = x`

The length of
`DC` is 20.

2) If
`QV = VP` and
`RW = WS`, then we can use the following proportionality ratio:

`(QP)/(QV) = (x-7)/(12-7)` (2)

Where
`x` is the length of segment
`\overline{PS}`.

If
`QP = 2\cdot QV`, then the value of
`x` is:

`2 = (x-7)/(5)`

`10 = x-7`

`x = 17`

The length of
`PS` is 17.