Question 184287
Let L = Length of rectangle
Let W = Width of rectangle
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We know:  "The length of a rectangular frame (L) is (=) 7cm more than (+) the width (W)" -> Equation 1: {{{ L = 7 + W }}}

We also know:  "The area inside the frame (L x W) is (=) 98 square cm" -> Equation 2: {{{ LW = 98 }}}
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Next, we can use Equation 1 to substitute (7 + W) for L in Equation 2:
{{{ LW = 98 }}}
Substitute:
{{{ (7+W)W = 98 }}}
Distribute the W:
{{{ 7W + W^2 = 98 }}}
Move everything to the left-hand side:
{{{ W^2 + 7W - 98 = 0 }}}
Factor the quadratic:
{{{ (W + 14)(W - 7) = 0 }}}
Solve:
{{{W + 14 = 0}}}    {{{W-7= 0}}}
{{{W = -14}}}       {{{W = 7}}}
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Since a width cannot be negative, that leaves us with <b>Width = 7cm</b>.
To check our answer, calculate our length by substituting back into Equation 1:
{{{ L = W + 7 }}}
{{{ L = 7 + 7 }}}
{{{ L = 14 }}}
Next, ensure the area is 98 square cm:
{{{ LW = 98 }}}
{{{ (14)(7) = 98 }}}
{{{ 98 = 98 }}}
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Hope this helps. ~ Joe