The diagonals of square abcd intersect at

e. if ae = 3x - 4 and bd = 10x - 48, find ac.

AC = 52

Step-by-step explanation:

the diagonals of a square are congruent and bisect each other, hence

AC = BD

2 (3x - 4) = 10x - 48

6x - 8 = 10x - 48 (subtract 10x from both sides)

- 4x - 8 = - 48 (add 8 to both sides)

- 4x = - 40 (divide both sides by - 4)

x = 10

⇒ AC = 2 (3 * 10 - 4) = 2 * 26 = 52