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salantis [7]
2 years ago
5

Kathy is fencing in her yard that has an area of 800 square feet. Her yard is in the shape of a rectangle where the length is 60

less than 5 times the width. Find the length and width
Mathematics
1 answer:
anygoal [31]2 years ago
7 0

Answer:

The dimensions of the yard are W=20ft and L=40ft.

Step-by-step explanation:

Let be:

W: width of the yard.

L:length.

Now, we can write the equation of that relates length and width:

L=5W-60 (Equation #1)

The area of the yard can be expressed as (using equation #1 into #2):

Area=W*L=W*(5W-60) (Equation #2)

Since the Area of the yard is 800 ft^2, then equation #2 turns into:

800=W*(5W-60)

Now, we rearrange this equation:  

800=W*(5W-60)//800=5W^2-60W//5W^2-60W-800=0

We can divide the equation by 5 :

W^2-12W-160=0

We need to find the solution for this quadratic. Let's find the factors of 160 that multiplied yields -160 and added yields -12. Let's choose -20 and 8, since (-20)*8=160 and -20+8=-12. The equation factorised looks like this:

(W-20)(W+8)=0

Therefore the possible solutions are W=20 and W=-8. We discard W=-8 since width must be a positive number. To find the length, we substitute the value of W in equation #1:

5*20-60=40

Therefore, the dimensions of the yard are W=20ft and L=40ft.

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