Quant Question Of The Day : 1
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Geometry
In the figure, ABCD is a rhombus. Point E is on the diagonal AC such that AE = 41, EC = 9 and measure of ∠ABE = 90º. Find the area of this rhombus.
Solution : Let’s say BD intersect AC at O .
BO² = AO × OE
[ OE = 1/2 AC – EC]
BO = √(25×16) = 20
Diagonal BD = 40
Area of the rhombus = 1/2 × Product of diagonals = 1/2 ×50 ×40 = 1000 square units.