1. ## Area Problem

Hello,
The Area of a rectangle is 360 square cm, if 12 is added to the length of the figure, and 5 is substracted from the width, the resulting Area is the same. What are the dimensions of the first rectangle?

Tried to solve it using a system of 2 equations but I'm confused about the "square cm".

2. Originally Posted by norifurippu
Hello,
The Area of a rectangle is 360 square cm, if 12 is added to the length of the figure, and 5 is substracted from the width, the resulting Area is the same. What are the dimensions of the first rectangle?

Tried to solve it using a system of 2 equations but I'm confused about the "square cm".

Let the length of the first rectangle be x.
Let the width of the first rectangle be y.

$\displaystyle xy=360$

$\displaystyle (x+12)(y-5)=360$

$\displaystyle xy-5x+12y-60=360$

$\displaystyle -5x+12y-60=0$

$\displaystyle 5x-12y+60=0$

$\displaystyle 5x-12*\frac{360}{x}+60=0$

$\displaystyle x-12*\frac{72}{x}+12=0$

$\displaystyle x^2+12x-864=0$

$\displaystyle (x+36)(x-24)=0$

$\displaystyle x=-36$ or $\displaystyle x=24$

Rejecting the negative root,

$\displaystyle x=24$ cm

$\displaystyle y=\frac{360}{24}=15$ cm

The dimensions of the first rectangle are 24 cm and 15 cm.

3. Thanks a lot!