A garden is measuring 12m by 16m is to have a path around it, increasing the total area to 285 square metre. what is the width of the path?
I went like that
(16+2x).(12+2x)= 285
4x^2+56x-93=0
I am stuck now
You're right.
By the way, the solutions of your your quadratic equations are:
x = - 31 / 2 and x = 3 / 2
Length can not be negative so x = 3 / 2 = 1.5 m
To solve the quadratic equation 4x^2 + 56x - 93 = 0, you can use the quadratic formula. The formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
In your case, a = 4, b = 56, and c = -93. Substituting these values into the quadratic formula, we get:
x = (-56 ± sqrt(56^2 - 4 * 4 * -93)) / (2 * 4)
Now, let's calculate the value under the square root:
x = (-56 ± sqrt(3136 + 1488)) / 8
x = (-56 ± sqrt(4624)) / 8
x = (-56 ± 68) / 8
Now, we have two possible solutions:
1. x = (-56 + 68) / 8 = 12 / 8 = 1.5
2. x = (-56 - 68) / 8 = -124 / 8 = -15.5
Since we are dealing with measurements, we discard the negative value. Hence, the width of the path is 1.5 meters.
To solve the quadratic equation 4x^2 + 56x - 93 = 0, we can use the quadratic formula. The quadratic formula states that for an equation ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, the equation is 4x^2 + 56x - 93 = 0, which means a = 4, b = 56, and c = -93. Plugging these values into the quadratic formula, we get:
x = (-56 ± √(56^2 - 4*4*(-93))) / (2*4)
Simplifying further, we have:
x = (-56 ± √(3136 + 1488)) / 8
x = (-56 ± √4624) / 8
x = (-56 ± 68) / 8
Now, we have two possible values for x:
x1 = (-56 + 68) / 8 = 12 / 8 = 1.5
x2 = (-56 - 68) / 8 = -124 / 8 = -15.5
Since the width of the path cannot be negative (as it represents a physical distance), we can discard x2 = -15.5 as a valid solution. Therefore, the width of the path is 1.5 meters.