Question

Length of the median of the trapezoid is . The median divides the trapezoid into two areas whose ratio is . The length of the shorter base is:

Answer 1

Answer:

Step-by-step explanation:

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