a rectangle has an area of 330m^2 , one side is 7 m longer than the other
what are the dimensions of this rectangle
To find the dimensions of the rectangle, we can use the information given.
Let's assume the length of the rectangle is "x" meters. Since one side is 7 meters longer than the other, the width of the rectangle will be (x + 7) meters.
The area of a rectangle is calculated by multiplying its length and width. We know that the area of the rectangle is 330 m². Thus, we can write the equation:
x * (x + 7) = 330
Expanding the equation, we get:
x^2 + 7x = 330
Rearranging the equation to simplify:
x^2 + 7x - 330 = 0
To solve this quadratic equation, we can either factorize it or use the quadratic formula. In this case, factoring the equation would be a bit difficult, so let's use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
For the equation x^2 + 7x - 330 = 0, the coefficients are:
a = 1
b = 7
c = -330
Substituting the values in the quadratic formula:
x = (-7 ± √(7² - 4 * 1 * -330)) / (2 * 1)
Now, we can simplify the formula:
x = (-7 ± √(49 + 1320)) / 2
x = (-7 ± √1369) / 2
x = (-7 ± 37) / 2
Now we have two values for "x," which are:
x₁ = (-7 + 37) / 2 = 30 / 2 = 15
x₂ = (-7 - 37) / 2 = -44 / 2 = -22
Since the length cannot be negative, we will disregard the value -22.
Therefore, the length of the rectangle is 15 meters, and the width is (15 + 7) = 22 meters.
To find the dimensions of the rectangle, we can set up an equation using the given information.
Let's assume the length of the rectangle is x meters. According to the problem, one side of the rectangle is 7 meters longer, so the width would be (x + 7) meters.
The formula for finding the area of a rectangle is length multiplied by width. In this case, the formula would be x * (x + 7) = 330 m².
Now, let's solve this equation to find the value of x:
x * (x + 7) = 330
Expanding the equation:
x² + 7x = 330
Rearranging the equation in standard quadratic form:
x² + 7x - 330 = 0
Now, we have a quadratic equation. We can solve it using factoring, completing the square, or using the quadratic formula. In this case, let's use factoring.
Factoring the equation:
(x + 22)(x - 15) = 0
Setting each factor to zero:
x + 22 = 0 or x - 15 = 0
Solving for x:
For x + 22 = 0:
x = -22
For x - 15 = 0:
x = 15
Since we can't have a negative length for a rectangle, we discard the negative solution. Therefore, the length of the rectangle is 15 meters.
Now, we can find the width by adding 7 meters to the length:
Width = Length + 7 = 15 + 7 = 22 meters.
So, the dimensions of the rectangle are 15 meters by 22 meters.
a = first side
b = second side
A = Area
b = a + 7
A = a * b
A = a * ( a + 7 )
A = a ^ 2 + 7 a
a ^ 2 + 7 a = 330
a ^ 2 + 7 a - 330 = 0
The exact solutions are:
a = -22
and
a = 15
The length can't be negative, so
a = 15 m
b = a + 7
b = 15 + 7
b = 22 m
A = a * b
A = 15 * 22
A = 330 m ^ 2
P.S.
If you don't know how to solve equation
a^2+7a-330=0
In google type:
quadratic equation online
When you see list of results click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula
When page be open in rectangle type:
a^2+7a-330=0
and click option:
solve it!
You wil see solution step-by-step