Question 951419: The width of a rectangular painting is 5 inches shorter than the length.
a. Write algebraic expressions to represent the width and the length of the painting.
b. Write an equation to model the area of the painting.
c. Solve the quadratic equation. What do the x-intercepts mean in respect to the problem situation?
I tried: What I know the w is 5 inches less than the length
w =w-l
l= w+5
subtract one from both side is 4
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The width of a rectangular painting is 5 inches shorter than the length.
a. Write algebraic expressions to represent the width and the length of the painting.
Length = x
Width = x-5
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b. Write an equation to model the area of the painting.
Area = length*width = x(x-5) = x^2-5x
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c. Solve the quadratic equation.
You must solve it for some particular value of the Area.
Do you have a particular value?
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What do the x-intercepts mean in respect to the problem situation?
If Area = x(x-5), the x-intercepts are the value of
x and x-5 that make the Area = 0
That occurs when x = 0 or x = 5
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If x = 0, the length is zero ; so the Area = 0
If x = 5, the width (which is x-5) = zero ; so the Area = 0
Cheers,
Stan H.
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