急 ! 急! F4 Quadratic Equations

9.(a)
The breadth of the original rectangle = 224/x

The breadth of the new rectangle = (224/x) + 1 = (224 + x)/x

9.(b)
The area of new rectangle = 224 + 1 = 225 cm^2

(x - 1)[(224 + x)/x]= 225
(x - 1)(224 + x) = 225x
224x - 224 + x^2 - x = 225x
x^2 - 2x - 224 = 0
(x - 16)(x + 14) = 0

x = 16
or
x = -14 (rejected)



10.(a)
Let h be the distance of the top end of the ladder from the ground

5^2 = 3^2 + h^2
25 = 9 + h^2
h^2 = 16
h = 4m

10.(b)
5^2 = (x + 3)^2 + (4 - x)^2
25 = x^2 + 6x + 9 + 16 - 8x +x^2
2x^2 - 2x = 0
x(x - 1) = 0

x = 1
or
x = 0 (rejected)


11.(a)
The new area
= (80 - 2x)(60 - 2x)
= 4800 - 280x + 4x^2

11.(b)
New area = (80)(60)(1/6) = 800 m^2

800 = 4800 - 280x + 4x^2
x^2 - 70x + 1000 = 0
(x - 20)(x - 50) = 0

x = 20
or
x = 50 (rejected since x < 30)


12.
Let x be the speed of current

Speed in upstream = 10 - x
Speed in downstream = 10 + x

18/(10 - x) + 28/(10 + x) = 5
18(10 + x) + 28(10 - x) = 5(10 + x)(10 - x)
180 + 18x + 280 - 28x = 500 - 5x^2
5x^2 - 10x - 40 = 0
x^2 - 2x + 8 = 0
(x + 2)(x - 4) = 0

x = -2 (rejected)
or
x = 4 km/h