Question

isosceles trapezoid jklm has legs JK and LM and base KL if JK=8x-9, kl=7x+10 and LM=10x+2 find the value of x

Answer 1

The domain:

`8x-9 > 0\to 8x > 9\to x > (9)/(8)\\\\7x+10 > 0\to 7x > -10\to x > -(10)/(7)\\\\10x+2 > 0\to 10x > -2\to x > -0.2\\\\D:x\in\left((9)/(8);\ \infty\right)`

If the trapezoid JKLM is an isosceles trapezoid then the legs are congruent.

`|JK|=|LM|\to 8x-9=10x+2\ \ \ |+9\\\\8x=10x+11\ \ \ |-10x\\\\-2x=11\ \ \ |:(-2)\\\\x=-5.5\\otin D`

Answer: Such a trapezoid does not exist.