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A rectangular Corn Hole area at the recreation center has a width of 5 feet and a length of 10 feet. If a uniform amount is added to each side, the area is increased to 84 square feet. What is the amount added to each

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Respuesta :

carlosego
1. The formula for calculate the area of a rectangle, is:
 
 A=LxW
 
 A is the area of the rectangle
 L is the length of the rectangle.
 W is the widht of the rectangle

2. You have that:
 
 -The rectangular Corn Hole area has a width of 5 feet and a length of 10 feet, so:
 
 L1=10 feet
 W1=5 feet
 
 - When a uniform amount is added to each side (x), the area is increased to 84 feet². Then, you have a different length (L2) and a different width (W2):
 
 3. The new length is: 
 
 L2=L1+x+x
 L2=L1+2x
 L2=10+2x
 
 4. The new width is:
 
 W2=W1+x+x
 W2=W1+2x
 W2=5+2x
 
 5. The new area is:
 
 A2=84 feet²
 
 6. Then, you have:
 
 A=LxW
 84=(10+2x)(5+2x)
 
 7. When you apply the distributive property, you obtain a quadratic equation:
 
 4x²+30x-34=0
 
 8. You can solve with by applyin the quadratic formula: 
 
 x=(-b±√(b^2-4ac))/2a
 
 a=4
 b=30
 c=-34
 
 9. Then, the answer is:
 
 x=1 feet
 
jtglobal

Answer:

I can't believe this guy above me has a verified answer and it is wrong.... anyway the true answer to this is 2. I checked it myself when I put 1 as the answer and got this question wrong, and it showed me the correct answer is 2 so don't believe the verified answer.

Step-by-step explanation:

Review Question #7:

The answer to this question is 2ft, not 1ft.

This is because:

So the width of the second rectangle can be represented by 10+2x, and the length of the second rectangle can be represented by 5+2x. Lets make 2x equal y to make things easier though. Because the product of both 10+2x and 5+2x is 84 square feet, we must multiply the two equations together first.

(10+y)(5+y)=84

This then equals:

50+10y+5y+y^2=84

Then add the like terms:

y^2+15y+50=84

Then set the equation to zero by subtracting 84 from both sides:

y^2+15y-34=0

From that, you can use the box method, or any method to get:

(y+17)=0 and (y-2)=0

Which would then simplify to:

y=-17 and y=2

However, we substituted y for 2x, so plug 2x into y:

2x=-17 and 2x=2

Then simplify from here:

x=-17/2 and x=1

The answer cannot be negative, so that means the answer is x=1, however, even though this is true, the answer is that 2ft was added to EACH SIDE, because the question was asking for what amount was added to each side.

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