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# GCSE maths question(s) watch

1. Can anybody tell me how to answer question 14 and 18 for this link:

http://www.aqa.org.uk/qual/gcse/qp-m...W-QP-Jun03.pdf

Thanks very much.
2. 14)

area of the rectangle = area of the triangle
(x+5)(x+2) = ½(x+8)x
multiply out
x²+3x-10 = ½x²+4x
take everything to one side
½x² - x - 10 = 0
multiply by 2
x² -2x - 20 = 0
3. (14)
Area of rectangle
= (x + 5)(x - 2)
= x^2 + 3x - 10

Area of triangle
= (1/2)(x + 8)x
= (1/2)x^2 + 4x

Since the areas are equal,

x^2 + 3x - 10 = (1/2)x^2 + 4x
(1/2)x^2 - x - 10 = 0
x^2 - 2x - 20 = 0

(18)
5x^2 + 14x - 3 = (x + 3)(5x - 1)

x^2 - 9 = (x + 3)(x - 3)

(5x^2 + 14x - 3) / (x^2 - 9)
= (x + 3)(5x - 1) / [(x + 3)(x - 3)]
= (5x - 1)/(x - 3)
4. 18)

(5x² + 14x - 3) / (x² + 9)

factorise top and bottom

(5x-1)(x+3) / (x-3)(x+3)
cancel common expressions
(5x-1)(x+3) / (x-3)(x+3)

(5x-1) / (x-3)

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