## 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.

Solve our previous question of the day :

Quant Question of the Day: 1

Shouldn’t it be BO^2= AO X OC and not BO^2= AO X OE????

Hello , Karan !

no,BO² = AO × OE is correct.

Triangle AOB and triangle BOE are similar triangles .

=> AO/BO = BO/OE

Hence , BO² = AO × OE

( It is true for every Right Angled Triangle , the perpendicular drawn from the vertex of a right angled triangle to its hypotenuse is geometric mean of the two parts of that it divides the hypotenuse into. )