1. ## Ratio problem

A rectangular patio measuring 6 meters by 8 meters is to be increased in size to an area of 150 square meters. If both the width and the length are to be increased by the same amount, what is the number of meters, to the nearest tenth, that the dimensions will be increased?

2. Originally Posted by ~berserk
A rectangular patio measuring 6 meters by 8 meters is to be increased in size to an area of 150 square meters. If both the width and the length are to be increased by the same amount, what is the number of meters, to the nearest tenth, that the dimensions will be increased?
Hello berserk,

We know tha the area of a rectangle is given by $\displaystyle A=l\cdot w$

Since we are going to increase the side lengths by the same value, lets call it x. The new dimentions are $\displaystyle l=6+x \\\ w=8+x$

Now pluggin all of this into the area formula we get

$\displaystyle 150=(6+x)(8+x) \iff 150 = 48+14x+x^2 =$

$\displaystyle x^2+14x-102=0$

From here just use the quadratic formula.

Good luck.

3. after I go through everything I get answers 5.3 and -19.3 which is extraneous how do i show the amount I need to increase by because when I do it by 5.3 it doesn't come out well, maybe I am doing something wrong?

4. Originally Posted by ~berserk
after I go through everything I get answers 5.3 and -19.3 which is extraneous how do i show the amount I need to increase by because when I do it by 5.3 it doesn't come out well, maybe I am doing something wrong?
5.3 is correct, but you need to remember that this is the length we increase them by so the new length and width are

11.3 and 13.3

$\displaystyle (11.3)(13.3)=150.29$