A quadrilateral has distinct integer side len | vedclass

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(B) Let the four distinct integer side lengths of the quadrilateral be $a, b, c,$ and $d$,where $a < b < c < d$.Given that the second-largest side $c

Vedclass · Accepted Answer

$26$

Vedclass · Answer

(B) Let the four distinct integer side lengths of the quadrilateral be $a, b, c,$ and $d$,where $a Given that the second-largest side $c = 10$,we have $a For the sides to be distinct integers,the largest possible values for $a$ and $b$ are $a = 8$ and $b = 9$.According to the polygon inequality theorem,the sum of any three sides of a quadrilateral must be greater than the fourth side.Thus,$a + b + c > d$.Substituting the values,we get $8 + 9 + 10 > d$,which simplifies to $27 > d$.Since $d$ must be an integer,the maximum possible value for $d$ is $26$.

$A$ quadrilateral has distinct integer side lengths. If the second-largest side has length $10$,then the maximum possible length of the largest side is

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