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Question

if the second largest side of quadrilateral is of length 10 then what is the length of largest side


Solution

Let a>b>c>d be the sides of the quadrilateral. Then b=10. The largest possible value for c is 10-1=9, and so the largest possible value for d is 9-1=8.

By the triangle inequality, a<b+c+d
a<10+9+8 =27 , so a=26.

(If a=27, you would get a line instead of a quadrilateral.)

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