Mrs. Henderson wants to build a fence around the rectangle or garden in her backyard in the scale drawing the perimeter of the g
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The dimensions of the rectangle can be a length of 2ft and a width of 4ft.
<h3>How to find the dimensions of the garden?</h3>
Remember that for a rectangle of length L and width W, the perimeter is:
P = 2*(L + W)
And the area is:
A = L*W
In this case, we know that the area is 8 square feet and the perimeter is 12 ft, then we have a system of equations:
12ft = 2*(L + W)
8ft² = L*W
To solve this, we first need to isolate one of the variables in one of the equations, I will isolate L on the first one:
12ft/2 = L + W
6ft - W = L
Now we can replace that in the other equation to get:
8ft² = (6ft - W)*W
This is a quadratic equation:
-W^2 + 6ft*W - 8ft² = 0
The solutions are given by Bhaskara's formula:
Then we have two solutions:
W = (-6 - 2)/-2 = 4ft
W = (-6 + 2)/-2 = 2ft
If we take any of these solutions, the length will be equal to the other solution.
So the dimensions of the rectangle can be a length of 2ft and a width of 4ft.
if you want to learn more about rectangles:
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<span>Reading the solution, please, look on the picture)
Let the side of the square will be X meters. This means that S1=x^2 </span>meters ^2<span>
One side of </span>new rectangular garden will be 2x meters and another (x-3) meters. So S2=2x(x-3) meters ^2
According to the <span>data:
</span><span>S1*1.25=S2
</span>x^2*1.25=<span>2x(x-3)
</span>1.25*x^2=2x^2-6x
0.75x^2-6x=0
3x^2-24x=0
x^2-8x=0
x(x-8)=0
x=8 or x=0
But x>0!
So x = 8 meters
The next question is to find S2.
S2=2x(x-3)=2*8*5=80 meters ^ 2
Let the side of the square will be X meters. This means that S1=x^2 </span>meters ^2<span>
One side of </span>new rectangular garden will be 2x meters and another (x-3) meters. So S2=2x(x-3) meters ^2
According to the <span>data:
</span><span>S1*1.25=S2
</span>x^2*1.25=<span>2x(x-3)
</span>1.25*x^2=2x^2-6x
0.75x^2-6x=0
3x^2-24x=0
x^2-8x=0
x(x-8)=0
x=8 or x=0
But x>0!
So x = 8 meters
The next question is to find S2.
S2=2x(x-3)=2*8*5=80 meters ^ 2