Question 235662: the width of a rectangular poster is one half of its length. the area of the poster is 128sq ft what is the width of the poster?
Found 2 solutions by stanbon, MathPro:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! the width of a rectangular poster is one half of its length. the area of the poster is 128sq ft what is the width of the poster?
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Let the length be x :
Then the width is x/2:
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Equation:
Area = length * width
128 = x*(x/2)
x^2 = 256
x^2-256 = 0
x^2-2^8 = 0
(x-2^4)(x+2^4) = 0
Positive Solution:
x = 16 ft.
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x/2 = 8 ft. (width)
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Cheers,
Stan H.
Answer by MathPro(14) (Show Source):
You can put this solution on YOUR website! Your problem is:
the width of a rectangular poster is one half of its length. the area of the poster is 128sq ft what is the width of the poster?
Let’s rewrite this as an equation. Call the width, W, and the length, L. The first sentence reads the width is L/2. This can be reworded as width is equal to L/2, so we get
W=L/2
In the second sentence we are told the area is 128 sq ft. Call the area A. The formula for the area is A = WL
Now we have two equations
W = L/2 equation(1)
A = WL equation(2)
Substitute for W from equation (1) into equation (2) to get:
A = (L/2)L = 128
Multiply both sides by 2:
L^2 = 256
Take the square root of both sides:
L = square root of (256)
Use the following notation, square root of a = sqrt(a)
In this notation L can be written as:
L = sqrt(256) = 16
Substitute for L into equation (1):
W = 16/2 = 8
Now we have W =8 and L= 16
Let’s check to see if our answer is correct:
Substitute the values for L and W into equation (2):
128 = ( 8)16
The left side is equal to the right side so our answer is correct.
Good Luck!
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