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

4. ABCD below is a rectangle. BE=6x+2 and ED=4x+6. Find the length of AC.-example-1

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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

User Jpaoletti
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