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CBSE Class 10 Answered

ABCD IS A TRAPEZIUM SUCH THAT AB IS PARALEL TO CD AND THE DIAGNLS INTERSECT AT A POINT 0.IF  OD=5CM, OB=7CM,AC=18CM, THEN THE DIFFERENCE BETWEEN THE LENGHTS OF OA AND OC IS EQUAL TO 1)3CM         2)6CM       3)8CM   4)12CM
Asked by seeni2005 | 21 Aug, 2020, 09:18: AM
answered-by-expert Expert Answer
In triangle OAB and triangle OCD,
Angle AOB = Angle COD ... (Vertically opposite angle)
Angle OAB = Angle OCD ... (Alternate angles)
So, triangle OAB is similar to triangle OCD ... (by AA similarity test)
Using the property of similarity i.e. corresponding sides of similar triangles are proportional, we have
 
OA over OC equals OB over OD equals 7 over 5 rightwards double arrow OA over OC equals 7 over 5 rightwards double arrow OA equals 7 over 5 OC AC equals AO plus OC equals 7 over 5 OC plus OC equals 12 over 5 OC 18 equals 12 over 5 OC rightwards double arrow OC equals 15 over 2 equals 7.5 space cm OA equals 7 over 5 cross times 15 over 2 equals 21 over 2 equals 10.5 space cm Difference space between space OA thin space and space OC thin space equals space OA minus OC equals 10.5 minus 7.5 space equals space 3 space cm
Answered by Renu Varma | 21 Aug, 2020, 11:17: AM

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