The length of a rectangle garden is (3x + 2) feet and its width is 2x feet. if the area of the garden is 170 square feet, what is the perimeter of the garden, in feet?

The perimiter is 54 feet

Step-by-step explanation:

First, we need to find the value of x.

To do this we need to multiply the two equations of the line becaise (length x width = area)

(3x + 2) x (2x)

(2x * 3x) + (2 * 2x)

6x² + 4x = 170

6x² + 4x - 170 = 0

We can then factorise this and solve because it is a quadratic:

2(3x² + 2x - 85)

2 (3x       )(x       )

You need to find the numbers that multiply to -85:

1,  -85

-1, 85,

-5, 17

-17, 5

We can eliminate the 1, 85, -1 and -85 factors and none of them are divisible by three, so we are then left with two:

-5, 17 and -17, 5

We can also eliminate -5 and 17 factors because when either are multiplied by three, the difference is not 2.

This means that the factors are:

2(x - 5)(3x + 17)

X = 5 or X = -17/3

x has to be 5 because we cannot have negatives in measurements

Now we know that 1x = 5, we can simply put this value into the equation for each side and multiply them both by two because in a rectangle, the two oposite sides are the same:

Side 1 = 3(5) + 2 = 17 x 2 = 34

Side 2 = 2(5 )= 10 x 2 = 20