Question 238005
4. ABCD is a rectangle. Find mB. 
All the angles of every rectangle are 90 degrees.<br> 
5. ABCD is a rectangle. AD = 3 and AB = 10. Find CD. 
AD and AB are the length and width of the rectangle. CD is the side opposite to    AB. Opposite sides of all rectangles are congruent so AB = CD = 10.<br>
6. ABCD is a rectangle. AC = 12. Find BE. 
BE? I think this is BD. If so, AC and BD are diagonals of the rectangle. Since the two diagonals of every rectangle are congruent, AC = BD = 12<br>
7. Find the value of x so that ABCD is a rectangle, if AD = 5x - 6 and BC = 3x + 4. 
This problem is incomplete. There is no way to solve it with the given information. Either you have left something out or the problem is invalid.<br>
However, we can find the value of x that makes AD = BC. This would make opposite sides equal which must be true if ABCD is a rectangle.<br>
To find an x that makes the opposite sides equal:
{{{5x-6 = 3x+4}}}
Now we solve this. Subtract 3x from each side:
{{{2x - 6 = 4}}}
Add 6 to each side:
{{{2x = 10}}}
Divide both sides by 2:
{{{x = 5}}}
So the only value for x that makes the opposite sides AD and BC equal is 5. If x is any other number ABCD cannot be a rectangle. But if x is 5, then ABCD could be but does not have to be a rectangle. (ABCD could also be a parallelogram or an isosceles trapezoid if x = 5.)<br>
In order to show that a quadrilateral is a rectangle we must show, directly or indirectly, that it is a parallelogram with 4 right angles. This cannot be done with the information you provided, regardless of the value(s) of x.