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 D 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