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Answers
Answer:
7 )) 20m x 5m or 10m x 10m
8a) x = -√3/2,-√3/2
8b) x = 1/2 , 3
Step-by-step explanation:
7 ))
Let 'A + 2B' be the 3 sides covered by the fence , where 2B is the 2 equal and opposite sides of the triangle.
Now,
A +2B = 30m
A= 30-2B...…(A)
now Area of rectangle => A x B = 100
=> (30 - 2B) x B = 100
=> 30B - 2B^2 = 100
=> -2(-15B + B^2) = 100
=> B^2 - 15B = -50
=> B^2 - 15B + 50 = 0
=> B^2 - 10B - 5B + 50B = 0
=> B ( B - 10) - 5(B - 10) = 0
=>(B-5)(B-10) = 0
=> B = (5,10) ….(B)
Inserting Value of B in A, we get
A = 30 - 2B
when B = 5
A = 30 - (2 x 5)
A = 30 - 10
A = 20
When B = 10
A = 30 - (2 x 10)
A = 30 - 20
A = 10
A has 2 values , hence,
A= (20,10)
now we have values of both A and B
A = (20,10)
B = (5,10)
Hence, the dimensions of the garden are
20m x 5m or 10m x 10m
8a)
4^2 + 4√3x + 3 = 0
4x^2 + 2√3x + 2√3x + 3 = 0
2x(2x+√3) + √3(2x +√3) = 0
(2x +√3)(2x +√3) = 0
x = (-√3/2,-√3/2)
8b)
2x^2 - 7x + 3
2x^2 -6x-1x + 3
2x(x - 3) -1 (x-3)
(2x-1)(x-3) = 0
x= (1/2 , 3)