Question

In a trapezium PQRS, PQ is parallel to RS, PQ = 20 cm, RS = 3 cm, PQR = 30o and QPS = 60o. What is the length of the line joining the midpoints of PQ and RS?

Answer 1

Midpoints of PQ and RS is basically the perpendicular height of the trapezium.

When you draw this diagram, you can see we can form two right triangles on either sides of the base. The perpendicular height (MN) of both the triangles is same and equal and also the required answer so by using trigonometric functions,

tan 30 = (MN)/x,
(x * tan 30) = MN

tan 60 = (MN)/(17 - x)
(17 - x) * tan 60 = MN

(x * tan30) = (17 - x) * tan 60
(x√3)/3 = 17√3 - x√3
x√3 = 51√3 - 3x√3
x = 51 - 3x
4x = 51
x = 51/4
x = 12.75

MN = (17√3)/4 cm