<h2>
Hope this helps!</h2>
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
<h3>So the perimiter is 34 + 20 = 54</h3>
<h2>Hope this helps!</h2>
