WAEC Mathematics Question 2015 ( Essay Question Two 2b )
May 19, 2020
By
Kings
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
.
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
