Question

The diagonals of rectangle ABCD intersect at point E. If AE = 2x + 5, and BD = 5x + 2, what is AC?

A. 21 units
B. 62 units
C. 42 units
D. 7 units

Answer 1

Answer:42 units

Explanation:

Answer 2

C. 42 units

Explanation:

I have attached a diagram to help you understand this problem. By looking at the diagram you can see that AE is half of BD, and that BD will be equal to AC. So we need to figure out the length of line BD to get AC.

To do this, you will multiply the length of AE by 2 and set it equal to BD.

`2(2x+5)=5x+2`

Then distribute, multiply what is in the parentheses by 2.

`4x+10=5x+2\\\\`

Subtract 4x from both sides.

`10=1x+2`

Subtract 2 from both sides.

`8=1x`

x = 8

Now that we have x, we can plug it into the equation to find BD.

`5 * 8 + 2=42`

BD is equal to 42 units, so we know...

AC = 42 units