SOLUTION: Consider kite ABCD with AB ≅ AD and BC ≅ DC. For kite ABCD, AB = x/6+ 8, AD = x/3+ 5, and BC = x − 2. Find x. Determine the length of each side of the kite. AB =

Algebra ->  Formulas -> SOLUTION: Consider kite ABCD with AB ≅ AD and BC ≅ DC. For kite ABCD, AB = x/6+ 8, AD = x/3+ 5, and BC = x − 2. Find x. Determine the length of each side of the kite. AB =       Log On


   

Question 1193076: Consider kite ABCD with
AB ≅ AD and BC ≅ DC.
For kite ABCD,
AB = x/6+ 8,
AD = x/3+ 5,
and BC = x − 2.
Find x.
Determine the length of each side of the kite.
AB =
AD =
BC =
DC =
Find the perimeter of ABCD.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

since given:
AB+=+x%2F6%2B+8
AD+=+x%2F3%2B+5
BC+=+x+-+2
and
AB ≅ AD and BC ≅ DC , we have

x%2F6%2B+8=x%2F3%2B+5
8-5=x%2F3-x%2F6++
3=2x%2F6-x%2F6++
3=x%2F6++
x=3%2A6
x=18

then,

AB+=+x%2F6%2B+8=18%2F6%2B8=3%2B8=11
AD+=+x%2F3%2B+5=18%2F3%2B5=6%2B5=11
BC+=+x+-2=18-2=16
BC+=+DC=16

and, the perimeter of ABCD is:
P=AB+%2BAD%2BBC%2BDC
P=11+%2B11%2B16%2B16
P=54