Maths F4...11

15.
(a)
Area of ΔPQC = (Area of square ABCD)- (Area of ΔAPQ) - (Area of ΔDQC) - (Area of ΔBPC)
(2x + 2)² - (1/2)x(x + 1) - (1/2)(2x+ 2)(x + 1) - (1/2)(2x + 2)(x + 2) = 35
2(2x + 2)² - x(x + 1) - (2x + 2)(x +1) - (2x + 2)(x + 2) = 70
(8x² + 16x + 8) - (x² + x) -(2x² + 4x + 2 - (2x² + 6x + 4) = 70
8x² + 16x + 8 - x² - x - 2x² -4x - 2 - 2x² - 6x - 4 = 70
(8 - 1 - 2 - 2)x² + (16 - 1 - 4 - 6)x + (8 -2 - 4 - 70) = 0
3x² + 5x - 68 = 0


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16.
(a)
Let x be the tens digit.
Then, the units digit = x + 2

Value of the two-digit number
= 10 * (tens digit) + (units digit)
= 10x + (x + 2)
= 11x + 2

(b)
11x + 2 = 3x(x + 2)
11x + 2 = 3x² + 6x
3x² - 5x - 2 = 0
(3x + 1)(x - 2) = 0
x = -1/3 (rejected) or x = 2
11x + 2 = 24

Hence, the two-digit number is 24.