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?

Question

5720 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-08T15:01:41

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

$l \times w = A$ $l xx w = A$

$(x + 3) (x + 5 + 3) = x (x + 5) + 60$ $(x + 3)(x + 5 + 3) = x(x + 5) + 60$

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

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

$6 x = 36$ $6x = 36$

$x = 6$ $x = 6$

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

Hopefully this helps!