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Given the Trapezoid ABCD

Find the length of AD

Pls hellpppp

Given The Trapezoid ABCD Find The Length Of AD Pls Hellpppp class=

Sagot :

Given:

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

To find:

The length of [tex]AD[/tex].

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 [tex]ABCD[/tex],

[tex]MN=\dfrac{AD+BC}{2}[/tex]

[tex]31x+1=\dfrac{30x-10+30x+28}{2}[/tex]

[tex]31x+1=\dfrac{60x+18}{2}[/tex]

[tex]31x+1=30x+9[/tex]

Isolate variable terms.

[tex]31x-30x=9-1[/tex]

[tex]x=8[/tex]

Now,

[tex]AD=30x-10[/tex]

[tex]AD=30(8)-10[/tex]

[tex]AD=240-10[/tex]

[tex]AD=230[/tex]

Therefore, the length of [tex]AD[/tex] is 230.

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