The Length Of A Swimming Pool Is 8m Longer Than Its Width And The Area Is 105 M2

The length of a swimming pool is 8m longer than its width and the area is 105 m2

 

Answer:

Let (x) be the width

Let (x + 8m) be the length

And (105) is the area

a = lw \\ 105 {m}^{2} = (x + 8m)(x) \\ i \: remove \: the \: units \: in \: order \: for \: you \: to \: easily \: understand\\ 105 = (x + 8)(x) \\ 105 = {x}^{2} + 8x \\ 0 = {x}^{2} +8 x - 105 \\ \\ {x}^{2} + 8x - 105 \\ factor \: it \\ (x + 15)(x - 7) \\ (x + 15) \\ x = - 15 \\ (x - 7) \\ x = 7 \\ we \: will \: choose \: the \: positive \: one \: because \: its \: a \: unit \\ x = 7 \\ width(x) = 7m \\ ength(x + 8) = (7 + 8) = 15m \\

To check:

a = lw \\ {105m}^{2} = (15m)(7m) \\ {105m}^{2} = {105m}^{2} \\ correct


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