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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?
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Expert:
Martin
replied 5 years ago.
Hello, welcome to Just Answer
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^288b+768=0
we then use the formula: X=(B + or  sqrt(B^24AC))/2A
on the shape AX^2+BX+C=0
so, solution = (88+sqrt(88^24*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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