# Find the width and the length if the length of a rectangle is 8 cm greater than the width. The area of the rectangle is 105 cm 2

Find the width and the length if the length of a rectangle is 8 cm greater than the width. The area of the rectangle is 105 cm 2
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Let x be the width of the rectangle and x+8 be the length.
$A=l×w$
$105=x\left(x+8\right)$
$105={x}^{2}+8x$
$0={x}^{2}+8x-105$
$0=\left(x+15\right)\left(x-7\right)$
$x=-15\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}7$
Since a negative length is impossible, the rectangle measures 7 centimetres by 15 centimetres.
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