# Originally a rectangle was twice as long as it is wide. When 4m were added to its length and 3m subtracted from its width, the resulting rectangle had an area of 600m^2. How do you find the dimensions of the new rectangle?

Apr 26, 2016

Original width $= 18$ metres
Original length $= 36$ mtres

#### Explanation:

The trick with this type of question is to do a quick sketch. That way you can see what is happening and devise a method of solution.

Known: area is $\text{width "xx" length}$

$\implies 600 = \left(w - 3\right) \left(2 w + 4\right)$

$\implies 600 = 2 {w}^{2} + 4 w - 6 w - 12$

Subtract 600 from both sides

$\implies 2 {w}^{2} - 2 w - 612 = 0$

$\implies \left(2 w - 36\right) \left(w + 17\right) = 0$

$\implies w = - 17$

It is not logical for a length to be negative in this context
so $w \ne - 17$

$w = 18$

$\implies L = 2 \times 18 = 36$

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Check

$\left(36 + 4\right) \left(18 - 3\right) = 40 \times 15 = 600 {m}^{2}$