(a) The mean of 1, 2, x, 11, y, 14, arranged in ascending order, 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 (Delta) LMN is 18(cm^{2}), find the area of the quadrilateral MPQN.
Explanation
(a) Mean (bar{x} = frac{sum x}{n} = 8)
(frac{1 + 2 + x + 11 + y + 14}{6} = 8)
(28 + x + y = 48 implies x + y = 20 …. (1) )
The middle numbers are x and 11 therefore, (frac{x + 11}{2} = 9)
(x + 11 = 18 implies x = 18 – 11 = 7)
Putting x = 7 in (1),
(7 + y = 20 implies y = 20 – 7 = 13)
(x, y) = (7, 13).
(b) (frac{LM}{LP} = frac{3}{4})
(frac{text{Area of LMN}}{text{Area of LPQ}} = frac{3^{2}}{4^{2}})
Area of (Delta) LPQ = (frac{16}{9} times 18 = 32 cm^{2})
(therefore text{Area of quadrilateral MPQN} = 32 – 18 = 14 cm^{2})