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Martin, Engineer

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1. Using 88 m of fence to enclose 384 m square of a rectangular

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1. Using 88 m of fence to enclose 384 m square of a rectangular plot of lawn. Find the dimension of the lawn. 2. The number of yd suqare in the area of a square is twice the number of yd in its perimeter. What is the measure of one side of the square, in yd?

For 1: let say the 2 perpendicular side of the rectangle are a and b.

2a + 2b = 88

a x b = 384

a = 384/b

2(384/b) + 2b = 88

we end up with the quadratic equation: 2b^2-88b+768=0

we then use the formula: X=(-B + or - sqrt(B^2-4AC))/2A on the shape AX^2+BX+C=0

so, solution = (-88+sqrt(88^2-4*2*768))/(2*2) = -12 As it's a dimension we take the positive. 12*b=384 ---> b=32 m so a=12 m dimension is 12m by 32m --------------------------------------------

Question 2. that one is easier.

1 side = a area = a*a perimeter=a+a+a+a

a*a=2(a+a+a+a) a^2=8a a = the solution = 8 yd as 8*8 = 64 and 64 is twice 8+8+8+8 (32)

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