The area of a new park in the shape of a square is 10x^2+7x12. What is the length of the side of th
Author : Carlos
Submitted : 20180614 04:25:01 Popularity:
Tags: shape park area square side
10x² + 7x  12 = (5x  4)(2x + 3)
5x  4 = 2x + 3 ... 3x = 7 ...x = (7/3)
the side = 5x  4 = 5(7/3)  4 = (35/3)  (12/3) = 23/3
the side = 2x + 3
10x² + 7x  12 = (5x  4)(2x + 3)
5x  4 = 2x + 3 ... 3x = 7 ...x = (7/3)
the side = 5x  4 = 5(7/3)  4 = (35/3)  (12/3) = 23/3
the side = 2x + 3 = 2(7/3) + 3 = (14/3) + (9/3) = 23/3.
Area = (sqrt(10x^2+7x12))^2
Length of the side = sqrt(10x^2+7x12)
s = side length of the square
s = √[10x^2+7x12]
The equation of the area of a square is:
A = s²
If the area is (10x² + 7x  12), we can solve for s as an expression in terms of x.
10x² + 7x  12 = s²
Let's make an expression for s:
s = ax + b
Then instead of squaring it, have it multiplied by itself, so we have:
10x² + 7x  12 = (ax + b)(ax + b)
And now we can expand the right side:
10x² + 7x  12 = a²x² + 2abx + b²
We can then compare the coefficients and see if we can do anything with it to try to solve for a and b:
a² = 10
2ab = 7
b² = 12
Here we have a problem since b² cannot be negative. So we cannot simplify this to be in the form of (ax + b)²
So the only thing we can do is leave it in this form:
s = √(10x² + 7x  12)
It's sqrt(10x^2 + 7x  12).
Noting that (3.1623x + a)^2 = 10x^2 + 6.32ax + a^2,
and that 7/6.32 = 1.1076,
you could say that the side would be only a little shorter than
3.1623x + 1.1076,
but that statement would be accurate only if x is quite large.


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