Question

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

Answer 1

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`