Question

the midline of a Trapezium is 10 cm and divides the area of the trapezium is the ratio 3 ratio 5 find the length of the basis of the trapezium

Answer 1

Given:  midline m = 10

and ratio of the divided areas = 3:5

Note: midline divides the trapezium exactly in the middle, so hight is equal for both the upper and lower parts of the trapezium.

    area of the trapezium = ( sum of bases x height ) /2

Answer:

    See the image first and then follow this,

  solve equation 1 and 2,

 (1)......         a+b   =  20

 (2)......       5a-3b   =  -20

multiply 3 to equation (1)

                 3a+3b = 60

                 5a-3b  = -20

                 __________

                 8a = 40                 = >         a=40/8 = 5

               ___________

therfore a =5 and b = 15       (substitute a in equation (1) to get b)

Let me know about the correctness of the answer