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Alex_Xolod [135]
3 years ago
12

The length of a rectangle is 2 foot less than 3 times its width. Find the the dimensions of this rectangle if the area is 96 squ

are feet.
Mathematics
1 answer:
Xelga [282]3 years ago
6 0
For example,area = a, length = l, width = w
First we write two equations. The easier equation is the area equation, which we know to be
a = l x w
So that the first equation is : 
<span>96 = l x w </span>

we make the second equation of the following statements :
<em>The length of a rectangle is 2 foot less than 3 times its width.</em>
<span>so it becomes :
l = 3w - 2
</span>
<span>To solve, we can use the substitution method. 
</span>
96 = l \times w\\96=(3w-2) \times w\\96=3w^{2}-2w\\3w^{2}-2w-96=0~~~~~~[now\ factor\ the\ equation]\\ (3w+16)(w-6)=0

3w+16=0\\3w=-16\\w= -\frac{16}{3}~~~~\Rightarrow~~~answer\ doesnt\ make\ sense\ , negative\ width.&#10;

w-6=0\\\boxed{w=6~~~~~~~\Rightarrow~~~~positive\ answer\ for\ width\ makes\ sense }&#10;

<span><em>So if our width is 6, Now substitute the value of w = 6 into equation 2 </em></span>

l=3w-2\\l=3(6)-2\\l=18-2\\l=16

So "w" = 6 and "l" = 16, and if we multiply them together, we get the correct area, 96. So our dimensions are 6 by 16.
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