Trapezoid side lengths

The circumference of the isosceles trapezoid is 34 cm. The difference in the length of the bases is 6 cm. The arm's length is one-third of the length of the longer base. Find the lengths of the trapezoidal sides.

Final Answer:

a = 15
b = 5
c = 9
d = 5

Step-by-step explanation:

a+b+c+d=34
b=d
a-c= 6
b = a/3

a+b+c+d = 34
b-d = 0
a-c = 6
a-3b = 0

Row 3 - Row 1 → Row 3
a+b+c+d = 34
b-d = 0
-b-2c-d = -28
a-3b = 0

Row 4 - Row 1 → Row 4
a+b+c+d = 34
b-d = 0
-b-2c-d = -28
-4b-c-d = -34

Pivot: Row 2 ↔ Row 4
a+b+c+d = 34
-4b-c-d = -34
-b-2c-d = -28
b-d = 0

Row 3 - -1/-4 · Row 2 → Row 3
a+b+c+d = 34
-4b-c-d = -34
-1.75c-0.75d = -19.5
b-d = 0

Row 4 - 1/-4 · Row 2 → Row 4
a+b+c+d = 34
-4b-c-d = -34
-1.75c-0.75d = -19.5
-0.25c-1.25d = -8.5

Row 4 - -0.25/-1.75 · Row 3 → Row 4
a+b+c+d = 34
-4b-c-d = -34
-1.75c-0.75d = -19.5
-1.1429d = -5.7143

d = -5.71428571/-1.14285714 = 5
c = -19.5+0.75d/-1.75 = -19.5+0.75 · 5/-1.75 = 9
b = -34+c+d/-4 = -34+9+5/-4 = 5
a = 34-b-c-d = 34-5-9-5 = 15

a = 15
b = 5
c = 9
d = 5

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