Finding the height and bases of a trapezoid

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jastomp

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Hello, could anyone help me with those two tasks?

1. The longer base of a trapezoid ABCD is AD, the diagonal is AC perpendicular to the leg CD and it is dividing the angle BAD in a half. The angle CDA = 600. The perimeter of a trapezoid is 80cm.
Find the bases of a trapezoid.
2. Equilateral trapezoidal lateral transverse lines intersect at right angles. The bases of a trapezoid are 5 and 11. Find the height of a trapezoid.
 
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jastomp said:
Hello, could anyone help me with those two tasks?

1. The longer base of a trapezoid ABCD is AD, the diagonal is AC perpendicular to the leg CD and it is dividing the angle BAD in a half. The angle CDA = 600. The perimeter of a trapezoid is 80cm.
Find the bases of a trapezoid.
2. Equilateral trapezoidal lateral transverse lines intersect at right angles. The bases of a trapezoid are 5 and 11. Find the height of a trapezoid.
Click to expand...

Sure. What have you done so far? What sort of help do you need?

I assume you have drawn a picture and marked some angles. Then you might have called CD "x" and found some other sides in terms of that.
 
Dr.Peterson said:
Sure. What have you done so far? What sort of help do you need?

I assume you have drawn a picture and marked some angles. Then you might have called CD "x" and found some other sides in terms of that.
Click to expand...
Yes, I did draw a picture, marked some angles and have called CD "x", but I haven't found other sides in terms of that. I have a few formulas, but I basically don't understand anything..
 
jastomp said:
Yes, I did draw a picture, marked some angles and have called CD "x", but I haven't found other sides in terms of that. I have a few formulas, but I basically don't understand anything..
Click to expand...
Can you please share the picture drawn by you? That would help us to determine the point where we can start to help you.
 
Hello, and welcome to FMH! :)

For the second problem (I am assuming the trapezoid is isosceles), I would use coordinate geometry. Let the 4 vertices be at:

[MATH]\left(-\frac{B}{2},0\right),\,\left(\frac{B}{2},0\right),\,\left(-\frac{b}{2},h\right),\,\left(\frac{b}{2},h\right)[/MATH]
fmh_0136.png

For the lateral transverse lines to be perpendicular, we require the product of the slopes of the transversals to be \(-1\).

What does the resulting equation imply?
 
You don't have to assume the trapezoid is isosceles; but it does turn out to be.

I started by looking at right triangle ACD, which is a special one.
 
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