Length of the median of the trapezoid is 10 inch. The median divides the trapezoid into two areas whose ratio is 3:5. The length of the shorter base is:
Answers
Given : Length of the median of the trapezoid is 10 inch.
The median divides the trapezoid into two areas whose ratio is 3:5.
To Find : The length of the shorter base is:
Solution:
Shorter Side = a
longer side = b
Median = (a + b)/2 = 10
=> a + b = 20
=> b = 20 - a
Area of trapezium with shorter base and Median = (1/2) ( a + 10) * h
Area of trapezium with longer base and Median = (1/2) ( b + 10) * h
two areas whose ratio is 3:5
=> (1/2) ( a + 10) * h : (1/2) ( b + 10) * h = 3 : 5
=> (a + 10) : (b + 10) = 3 : 5
=> (a + 10)/ (b + 10) = 3/5
=> 5a + 50 = 3b + 30
=> 5a + 20 = 3b
=> 5a + 20 = 3(20 - a)
=> 5a + 20 = 60 - 3a
=> 8a = 40
=> a = 5
The length of the shorter base is: 5 inches
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Answer:
5
Step-by-step explanation:
5