# A rectangle is 5 cm longer than it is wide. If the length and width are both increased by 3 cm, its area is increased by 60 cm2. How do you find the dimensions of the original rectangle?

Nov 8, 2016

Let the width be $x$ and the length $x + 5$.

$l \times w = A$

$\left(x + 3\right) \left(x + 5 + 3\right) = x \left(x + 5\right) + 60$

$\left(x + 3\right) \left(x + 8\right) = {x}^{2} + 5 x + 60$

${x}^{2} + 3 x + 8 x + 24 = {x}^{2} + 5 x + 60$

$6 x = 36$

$x = 6$

Hence, the width of the original rectangle was $6$ and the length was $11$.

Hopefully this helps!