WAEC Mathematics Question 2015 ( Essay Question Two 2b )

The diagram shows a rectangle PQRS from which a square of side cm has been cut. If the area of the shaded portion is 484. Find the value of .

  Solution 

Given PQRS is a rectangle,

i.e. PS = QR = 20cm and

PQ = SA + CD + BR

Assuming the cut off section is labeled ABCD

  PQ = 10 +  + 10

 PQ = (20+) cm

The diagram becomes;

But the area of the complete rectangle, i.e. PQRS = L X B

PQRS = (20 + ) x 20

PQRS = (400 + 20)

From the diagram, the cut-off section represents a square of sides ABCD

  Area of a square = L X L

= X 

=

Area of the shaded portion is obtained when a square is cut-off from the rectangle.

i.e (400 + 20) -  = 484

-  + 20 + 400 = 484

Collecting like terms

-  + 20 = 484 – 400

-  + 20 = 84

Multiplying both sides by (-) minus sign, we have:

 - 20 = -84

 - 20 + 84 = 0 …………. (Quadratic Equation)

 

Solving the quadratic equation using factorization method, we have:

 - 14 – 6 + 84 = 0

Grouping

(  - 14) - (6  - 84) = 0

( - 14) - 6(  - 14) = 0

(  - 14) (  - 6) = 0

  - 14 = 0        or                      - 6  = 0

  =14       or                     = 6

ANSWERED

DOWNLOAD PAGE 1

DOWNLOAD PAGE 2

DOWNLOAD PAGE 3