Question

Given the Trapezoid ABCD

Find the length of AD

Pls hellpppp

Answer 1

Given:

In trapezoid
`ABCD, AD\parallel BC, MN` is the mid-segment of
`ABCD, AD=30x-10,MN=31x+1,BC=30x+28`.

To find:

The length of
`AD`.

Solution:

We know that the length of the mid-segment of a trapezoids is half of the sum of lengths of two parallel sides of the trapezoid.

In trapezoid
`ABCD`,

`MN=(AD+BC)/(2)`

`31x+1=(30x-10+30x+28)/(2)`

`31x+1=(60x+18)/(2)`

`31x+1=30x+9`

Isolate variable terms.

`31x-30x=9-1`

`x=8`

Now,

`AD=30x-10`

`AD=30(8)-10`

`AD=240-10`

`AD=230`

Therefore, the length of
`AD` is 230.