Question

Work must be shown for this problem! The figure shown below is a rectangle. Make sure to solve for x and BD. Give both answers below.

Answer 1

x=10 and BD=74

Explanation:

In a rectangle, the two parts of the diagonals are always equal to each other. This means that AE=CE=BE=ED.

So, if AE is 3x+7, this means DE and BE are also 3x+7, so BD is twice that, or 2(3x+7) which when you multiply it is 6x+14.

Oh, also, since it says CE=37, this means that 3x+7=37

3x+7=37

-7 -7

3x=30

x=10

Now that you know that BD is 6x+14, and x is 10, simply multiply it.

6(10)+14=BD

60+14=BD

74=BD

Answer 2

x = 10

BD = 74

Explanation:

Find x by setting 3x+7 equal to 37. Solve for x by subtracting 7 on both sides then divide by 3 to get x=10.

Since 37 is half of AC, multiply that by 2 to find AC or BD, which are the exact same length of 74.