Question

What is the length of each segment in a trapezoid TUVW?

Answer 1

`UV=8\ units`

`XY=16\ units`

`TW=24\ units`

Explanation:

we know that

In this problem

XY is the mid-segment of trapezoid TUVW (because K is the midpoint segment TU and Y is the midpoint segment VW)

Remember that the length of the mid-segment is the sum of the two parallel bases divided by 2

so

`XY=(UV+TW)/(2)`

substitute the given values

`3x+7=(3x-1+8x)/(2)`

solve for x

Multiply by 2 both sides

`6x+14=11x-1`

`11x-6x=14+1`

`5x=15`

`x=3`

Find the length segment UV

`UV=3x-1`

substitute the value of x

`UV=3(3)-1=8\ units`

Find the length segment XY

`XY=3x+7`

substitute the value of x

`XY=3(3)+7=16\ units`

Find the length segment TW

`TW=8x`

substitute the value of x

`TW=8(3)=24\ units`