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Question

In given quadrilateral ABCD, BE = 3 cm and DF = 4 cm. find the length of AC if area of ABCD is 28cm2

A
4 cm
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B
6 cm
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C
7 cm
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D
8 cm
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Solution

The correct option is C 8 cm
Area of ABC = 12×base×height
= 12×AC×BE
Similarly
Area of ADC = 12×AC×DF

Area of quadrilateral ABCD =
Area of ABC
+ Area of ADC
Area of quadrilateral ABCD
28 = 12×AC×BE + 12×AC×DF
28 = 12×AC×(BE+DF)
28 = 12×AC×(3+4) = 12×AC×(7)
28×27 = AC = 8 cm

Length of AC is 8 cm.

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