Find the length of side AB of a trapezium ABCD. | DA⊥AB, CB⊥AB, AC ⊥ BD, BC = √13 ; CD = √1183.

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In this video tutorial, we will learn how to find the unknown side AB of a given trapezium ABCD (Trapezoid). We are given the lengths of two sides, BC = √13 and CD = √1183. Sides BC and AB are perpendicular, DA and AB are perpendicular. Diagonals AC and BD are mutually perpendicular.

#Similarity_in_right_triangles
#Pythagorean_Theorem
#Geometric_Mean

Useful for :

#NTSE, #GRE, #IITJEE, #IOQM, #RMO, #INMO, #ISI, #CMI, #MAT, #CAT, #SAT, #BITSAT, #PET, #CET, #MCA, #NDA, #CDS, #SSC, #KVPY, #RRB, #PO, etc
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The figure is out of scale. One way to solve the problem is as follows: let AD=y and AB=x then (y-sqrt(13))^2+x^2=1183 and from the condition of AC-BD perpendicularity we have x^2=sqrt(13)*y. Solving these two equations for x we obtain x=AB=sqrt(130).

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