Question 184287: The length of a rectangular frame is 7cm more than the width. The area inside the the frame is 98 square cm. Find the width of the frame. Answer by MathGuyJoe(20) (Show Source):
We know: "The length of a rectangular frame (L) is (=) 7cm more than (+) the width (W)" -> Equation 1:
We also know: "The area inside the frame (L x W) is (=) 98 square cm" -> Equation 2:
Next, we can use Equation 1 to substitute (7 + W) for L in Equation 2:
Substitute:
Distribute the W:
Move everything to the left-hand side:
Factor the quadratic:
Solve:
Since a width cannot be negative, that leaves us with Width = 7cm.
To check our answer, calculate our length by substituting back into Equation 1:
Next, ensure the area is 98 square cm:
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