SOLUTION: Triangle EWS has a perimeter of 26 and SE = 1/2 WE. The midsegment parallel to WS = 4. Find the lengths of the three sides of this triangle. thank you soo much

Question 147485: Triangle EWS has a perimeter of 26 and SE = 1/2 WE. The midsegment parallel to WS = 4. Find the lengths of the three sides of this triangle.
thank you soo much
Answer by aswathytony(47) (Show Source): You can put this solution on YOUR website!
given perimeter of triangle = 26 i.e, sum of length of three sides of triangle is 26.
i.e. WE + WS + SE = 26 ............(1)
given SE = 1/2 WE or WE = 2 SE........(2)
ALSO mid segment parallel to WS is 4 .
we know The segment that joins the midpoints of two sides of a triangle is parallel to the third side and has a length equal to half the length of the third side.
i.e. mid segment length is 4 then side parallel to it ; WS = 2 * 4 = 8....(3)
subsituting (2) & (3) in (1), we get
2 SE + 8 + SE = 26
3 SE + 8 = 26
3SE = 26- 8
= 18
SE = 18 / 3 = 6
2SE = WE ( from (2) )
i.e WE = 2 * 6 = 12
so length of three sides of the triangle are 6,8,12.
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