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 $ABCD$,

$MN=\dfrac{AD+BC}{2}$

$31x+1=\dfrac{30x-10+30x+28}{2}$

$31x+1=\dfrac{60x+18}{2}$

$31x+1=30x+9$

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.