4. ABCD below is a rectangle. BE=6x+2 and ED=4x+6. Find the length of AC.

Question

asked Jul 1, 2022 106k views

1 Answer

Jpaoletti · Answer 1 · 2022-07-04T12:42:16+0000

Answer:

28 units

Explanation:

ABCD is a rectangle. AC and BD are diagonals intersecting at point E.

Diagonals of a rectangle bisect each other.

$\therefore BE = ED$

$\therefore 6x + 2 = 4x + 6$

$\therefore 6x - 4x= 6-2$

$\therefore 2x= 4$

$\therefore x= (4)/(2)$

$\therefore x= 2$

$\therefore 6x + 2= 6*2+2= 12+2= 14$

$\therefore BE= 14\: units$

$\because BD = 2BE$

$\therefore BD = 2(14)= 28\: units$

$\because AC = BD$ (diagonals of a are equal in measure)

$\therefore AC = 28\: units$