Length 26

The length of the median of the trapezoid is 10 inches. The median divides the trapezoid into two areas whose ratio is 3:5. The length of the shorter base is:

Correct answer:

c =  5 in

Step-by-step explanation:

m=10 in S1​:S2​ = 3:5  (a+c)/2 = m a+c = 2⋅ m = 20  in  h1​=h2​ h1​+h2​=h  S1​ = h1​⋅ (a+m)/2 S2​ = h2​⋅ (c+m)/2 = h1​⋅ (c+m)/2  h1​⋅ (c+m)/2 : h1​⋅ (a+m)/2 = 3:5  (c+m) : (a+m) = 3:5  (c+m)=53​⋅ (a+m) (a+c)/2=m (c+10)=53​⋅ (a+10) (a+c)/2=10  (c+10)=3/5⋅ (a+10) (a+c)/2=10  3a−5c=20 a+c=20  Row2−31​⋅ Row1→Row2 3a−5c=20 2.67c=13.33  c=2.6666666713.33333333​=5 a=320+5c​=320+5⋅ 5​=15  a=15 c=5=5 in

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