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Question

In the figure, ABCD is a parallelogram and AB = 6 cm. If the area of triangle ADE is 34 that of parallelogram ABCD, then find the length of BE.


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Solution


Let the length of BE be y cm. Let the height from D to the base AB be h cm.

Area of triangle ADE
=34×area of ABCD

AE = AB+BE = (6 + y) cm.

Area of a triangle is half the product of base and height = 12AE×height = 12×(6+y)×h

Area of parallelogram is product of base and height = AB×height = 6 x h
Therefore,
12×(6+y)×h=34×6×h

6+y=2×34×6

6+y=9

y=3

The length of BE is 3 cm.


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