Theory question 109
Measures of Central Tendency(a) The mean of 1, 2, x, 11, y, 14 is 8 and the median is 9. Find the values of x and y.
(b) In the diagram, MN||PQ, |LM| = 3cm and |LP| = 4cm. If the area of ΔLMN is 18cm2, find the area of quadrilateral MPQN.
Show the model answer
Model answer
(a) Sum = 6 × 8 = 48, so x + y = 20.
With x < 11 < y the order is 1, 2, x, 11, y, 14 and the median = (x + 11)/2 = 9, so x = 7 and y = 13.
(b) Triangles LMN and LPQ are similar with ratio 3 : 4, so areas are in ratio 9 : 16.
Area LPQ = 18 × 16/9 = 32 cm2; area MPQN = 32 − 18 = 14 cm2.
Explanation
Areas of similar figures are in the ratio of the squares of their sides.