Linear and Quadratic Equations ACTIVITY ACTION CTION
Using techniques for modelling quadratic problems
OBJECTIVE To learn some basic techniques to aid the modelling of quadratic problems and hence solve them
Y 4
Steps for mathematical modelling (word problems)
The steps used for modelling problems leading to quadratic equations are the same used for modelling problems leading to linear equations.
1. Read the problem carefully and draw a diagram, if appropriate. 2.
3. Translate the word problem into an equation. 4. Solve the equation. 5. List all answers.
EXAMPLE 19
The perimeter of a rectangular garden is 36 m. If its area is 72 m2, fi nd the length and breadth of the garden.
Solution 1. Area = Length × Breadth
A = 72 l
2. Let l = length of the garden l + b = 18 b = (18 – l)
b
3. A = l × b A = l(18 – l ) = 72
4. 18l – l 2 = 72 l 2 – 18l + 72 = 0 (l – 6)(l – 12) = 0 ∴ l = 6, 12 l = 6
5. b = 12
Assign a variable to one of the quantities to be found and hence assign variables to the other quantities.
5
l = 12 b = 6
Answer: 12 m and 6 m
EXAMPLE 20
A rectangular metal frame has an area of metal of 76 cm2 as a border. If the dimensions of the glass on the inside of the frame are 10 cm × 5 cm, fi nd the uniform width of the frame.
