Answer:
Width = 11 yards
Length = 17 yards
Step-by-step explanation:
First of all, the length of the rectangle is 6 yards longer than the width, this means, length = width + 6 yards. This dimensions can be represented on figure 1, where w is width, and l, for length.
We know the area of a rectangle is A = width x length
For our case 187 = w . (w + 6)
Using the Distributive Property for the multiplication we obtain
[tex]187 = w^{2} +6w[/tex]
[tex]w^{2} +6w-187 =0,[/tex]
Using the quadratic formula [tex]w=\frac{-b\±\sqrt{b^{2}-4ac } }{2a}[/tex] where a = 1, b = 6, c = - 187 and replacing into the formula, we will have:
[tex]w=\frac{-6\±\sqrt{6^2-4(1)(-187)} }{2(1)}[/tex]
[tex]w=\frac{-6\±\sqrt{36+748} }{2}=\frac{-6\±\sqrt{784} }{2}=\frac{-6\±28}{2}[/tex]
We have two options: [tex]w=\frac{-6+28}{2}=\frac{22}{2}=11 yards[/tex]
Or
[tex]w=\frac{-6-28}{2}=\frac{-34}{2}=-17 yards[/tex] But a distance (width) can not be negative so, this answer for w must be discarded.
The answer must be width = 11 yards.
To find the length [tex]l =\frac{187}{11}=17 yards[/tex]
