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This question confuses me:
the length of a rectangle is 8 inches more than the width. If 4 inches is taken from the length and added to the width, the figure becomes a square with an area of 275.56 sq inches. What are the dimensions of the original figure?
 
word problems tend to confuse me, help would be greatly appreciated.
 
(step by step process if possible)
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4 Answers

Yay - no equations - The easiest way i found is this:

 
It became a square of area 275.56 so first take the square root of 275.56 which is 16.6.  
That is the new length and width.
 
Now do the opposite if what they did:
 
    subtract 4 to get the original width of 12.6 and add 4 to 16.6 to get the original length of 20.6.
 
your answer is L = 20.6 units,  W = 12.6 units.  woohoo!!
Hello Addie, 
 
We know that the width of the rectangle is unknown - this will be our variable x
 
We know that the length is 8 more than the width - the expression x + 8 represents the length
 
From what you told us, we are to take 4 inches from the length and then add it to the width. 
This gives us a square because we now have a rectangle that measures x +4 in length and x + 4
in width. You also said that the area of the new square is 275.56 in2. The formula for area looks
like this 
 
275.56 = (x + 4)(x + 4)       the next thing that we do is foil the right side.
 
275.56 = x2 +4x + 4x + 4*4  simplify and combining like terms give
 
275.56 = x2 + 8x + 16         at this point we want to bring the 275.56 over to the right side of the equation
 
0 = x2 + 8x + -259.56         in this form, we can use the quadratic formula to solve for x
 
x = (-b + sqrt(b2 - 4ac))/2a 
 
x = (-8 + sqrt(82 - 4 (1)(-259.56)))/2
 
x = 12.6
 
Now that we know what x equals, we can go back and substitute it into the original expression. When we do that we get 12.6 + 8 = 20.6 for the length, and 12.6 for the width. 
 
I hope this helps.
 
Ishmael Patterson

Comments

Note that when you have a complete square, (x+4)²=275.56 in this case, there is no need to foil it out and use the quadratic formula: you can simply take the square root on both sides.
Note that when there is a complete square on one side of the equation, (x+4)²=275.56 in this case, there is no need to foil it out and use the quadratic equation: you can simply take the square root on both sides of the equation.
 JUst choose a variable for unknown, what problem asking you to find out.
 
     X = width
     X +8 = length
 
      X+ 8 -4 = X+4      4 is taken from the length
 
      X + X+4 = 2X +4  New width
 
        (2X +4) 2 = 275.56  Now you can solve the quadratic.
     
       Always choose a variable for unknown( what problem asking you to find out), then convert the English statements to Algebraic Expression, and you won't get confused.      
Let's translate each sentence into an equation, with L and W being the length and width of the original rectangle:
 
the length of a rectangle is 8 inches more than the width: L=W+8
 
If 4 inches is taken from the length and added to the width, the figure becomes a square:
In a square, length and width are equal, so L-4=W+4 (same statement as the first sentence)
 
...with an area of 275.56 sq inches: area of a square is side length squared, so
(L-4)²=(W+4)²=275.56
 
Now take the square root on all three terms and get
L-4=W+4=√275.56=16.6 (We only need the positive square root, since lengths are always positive.)
 
So, L=16.6+4=20.6 and W=16.6-4=12.6 are the length and width of the original rectangle.