(2s + 3)2 - 24 = s2
4s2 + 12s + 9 - 24 = s2
3s2 + 12s - 15 = 0
s2 + 4s - 5 = 0
(s + 5)(s - 1) = 0
s + 5 = 0
s = -5
We disregard this answer because we don't measure in negatives.
s - 1 = 0
s = 1
The smaller square is 1 yd x 1 yd
2(1) + 3 = 5
The larger square is 5 yds by 5 yds.
David W.
tutor
If s = the length of a side if the smaller square, the larger square has sides of 2s + 3.
Area = length of a side squared. The larger square has 24 extra square yards.
(2s + 3)(2s + 3) - 24 = s2
4s2 + 12s + 9 - 24 = s2
3s2 + 12s - 15 = 0
To make the equation easier to factor, I divided it by 3.
s2 + 4s - 5 = 0
Then I factored the left side.
(s + 5)(s - 1) = 0
In order for the left side to equal 0, one of the factors has to equal 0.
s + 5 = 0
s = -5
As mentioned, we disregard this solution.
s - 1 = 0
s = 1
So, the length of a side of the small square is 1, making the dimensions 1 yd x 1 yd.
2(1) + 3 = 5, so the large square is 5 yds x 5 yds.
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10/04/18
Kat M.
10/04/18