The area of a rectangle is 48 square cm. If the length is 8 cm greater than the width, what are the dimension of the rectangle?
(w+8)w=48
solve for w
w = width
l = length
A = Area
l = w + 8
A = l * w
A = ( w + 8 ) * w = 48
w ^ 2 + 8 w = 48 Subtract 48 to both sides
w ^ 2 + 8 w - 48 = 48 - 48
w ^ 2 + 8 w - 48 = 0
The exact solutions are :
w = 4
and
w = - 12
Width can't be negative so :
w = 4 cm
l = w + 8
l = 4 + 8 = 12 cm
A = l * w
A = 12 * 4 = 48 cm ^ 2
P.S.
If you don't know how to solve equation :
w ^ 2 + 8 w - 48 = 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:
w ^ 2 + 8 w - 48 = 0
and click option: solve it
You will see solution step-by step
Step 1: Let's assume the width of the rectangle is 'x' cm.
Step 2: According to the problem, the length is 8 cm greater than the width, so the length would be 'x + 8' cm.
Step 3: The formula for the area of a rectangle is given by the product of its length and width, so we can set up the equation: (x + 8) * x = 48.
Step 4: Simplifying the equation, we have x^2 + 8x = 48.
Step 5: Rearranging the equation in standard form, we get x^2 + 8x - 48 = 0.
Step 6: Factoring the quadratic equation, we have (x + 12)(x - 4) = 0.
Step 7: Setting each factor equal to zero and solving for 'x', we find x = -12 or x = 4.
Step 8: Since the width of a rectangle cannot be negative, we can discard the solution x = -12.
Step 9: Therefore, the width of the rectangle is 4 cm.
Step 10: Using the length formula from Step 2, the length of the rectangle is x + 8 = 4 + 8 = 12 cm.
Step 11: In conclusion, the dimensions of the rectangle are 4 cm (width) and 12 cm (length).
To solve this problem, let's first establish the variables. Let's say that the width of the rectangle is "x" cm. This means that the length will be "x + 8" cm, as it is 8 cm greater than the width.
The formula for the area of a rectangle is given by "length x width". In this case, the area is given as 48 square cm. So we can write the equation as:
Length x Width = 48
Substituting the values we have:
(x + 8) x x = 48
Now we can simplify the equation:
x(x + 8) = 48
Expanding the equation:
x^2 + 8x = 48
Rearranging the equation to bring it to a quadratic form:
x^2 + 8x - 48 = 0
Now we can solve this quadratic equation by factoring or using the quadratic formula. In this case, let's use factoring.
We need to find two numbers whose product is -48 and whose sum is 8. After trial and error, we find that the numbers are 12 and -4.
Therefore, the factored equation is:
(x - 4)(x + 12) = 0
Now we set each factor equal to zero:
x - 4 = 0 or x + 12 = 0
Solving for x:
x = 4 or x = -12
Since the width of a rectangle cannot be negative, we can discard the solution x = -12.
Therefore, the width of the rectangle is x = 4 cm. Substituting this back into the original equation, we find that the length is x + 8 = 4 + 8 = 12 cm.
So, the dimensions of the rectangle are width = 4 cm and length = 12 cm.