SOLUTION: 4. ABCD is a rectangle. Find mB. A. 45° B. 90° C. 100° D. 180° 5. ABCD is a rectangle. AD = 3 and AB = 10. Find CD. A. 3 B. 6 C. 10

Algebra ->  Formulas -> SOLUTION: 4. ABCD is a rectangle. Find mB. A. 45° B. 90° C. 100° D. 180° 5. ABCD is a rectangle. AD = 3 and AB = 10. Find CD. A. 3 B. 6 C. 10       Log On


   

Question 238005: 4. ABCD is a rectangle. Find mB.


A. 45°
B. 90°
C. 100°
D. 180°
5. ABCD is a rectangle. AD = 3 and AB = 10. Find CD.


A. 3
B. 6
C. 10
D. 20
6. ABCD is a rectangle. AC = 12. Find BE.


A. 6
B. 8
C. 10
D. 12

7. Find the value of x so that ABCD is a rectangle, if AD = 5x – 6 and BC = 3x + 4.


A. 3
B. 4
C. 5
D. 6

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
4. ABCD is a rectangle. Find mB.
All the angles of every rectangle are 90 degrees.

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.

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

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.

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.

To find an x that makes the opposite sides equal:
5x-6+=+3x%2B4
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.)

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.