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If angle of a triangle are in AP and the length of the two larger sides of the triangle are 10 and 9 units then find the length of the smallest side? 

Asked by Sumantkashyap1111 6th July 2018, 2:11 PM
Answered by Expert
Answer:
Let angles of the triangle be a - d, a, a + d
a - d + a + a + d = 180°
3a =  180°
a = 60°
Hence, angles of the triangle are 30°, 60°, 90°.
Let third side be x.
begin mathsize 16px style Using space cosine space rule comma
cos 60 degree equals 1 half
fraction numerator straight x squared plus 10 squared minus 9 squared over denominator 2 cross times straight x cross times 10 end fraction equals 1 half
straight x squared plus 100 minus 81 equals 10 straight x
straight x squared minus 10 straight x plus 19 equals 0
straight x equals fraction numerator 10 plus-or-minus square root of 100 minus 4 cross times 1 cross times 19 end root over denominator 2 end fraction equals 5 plus-or-minus square root of 6
Hence comma space the space smallest space side space of space the space triangle space is space 5 space minus space square root of 6.
end style
Answered by Expert 10th July 2018, 9:24 AM
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