Question

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?

Answer 1

Hope this helps!

Answer:

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

So the perimiter is 34 + 20 = 54

Hope this helps!