SOLUTION: An isosceles trapezoid has a perimeter of 51 kilometers. Its shorter base measures 7 kilometers and its longer base measures 14 kilometers. The two remaining sides have the same le

Question 531229: An isosceles trapezoid has a perimeter of 51 kilometers. Its shorter base measures 7 kilometers and its longer base measures 14 kilometers. The two remaining sides have the same length; what is that length?
Answer by shivang jindal(3) (Show Source): You can put this solution on YOUR website!
Solution:
Let OA = a
OB = b,
OC = c,
OD = d,
OE = e,
OF = f,
[OAB] =x,
[OCD] = y,
[OEF] = z,
[ODE] = u,
[OFA] = v
[OBC]= w.
We are given that v^2 = zx, w^2 = xy and we have to prove that u^2 =yz.
Since∠AOB =∠DOE, we have
u\x =(1/2 de sin∠DOE)/(1/2 ab sin∠AOB)= de/ab
Similarly, we obtain
v/y =fa/cd
w/z =bc/ef
Multiplying, these three equalities, we get uvw =xyz. Hence
x^2 * y^2 * z^2 =u^2*v^2*w^2 =u^2 (zx)(xy).
This gives u^2=yz, as desired.

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