The length of the top of a work bench is 5 m greater than the width. The area is 66 m^2. Find the length and the width.
Whats your answer then we will check it.
L = the length
W = the width
A = the area
L = W + 5
A = L ∙ W
66 = ( W + 5 ) ∙ W
66 = W² + 5 W
Subtract 66 to both sides
66 - 66 = W² + 5 W - 66
0 = W² + 5 W - 66
W² + 5 W - 66 = 0
The solutions are:
W = - 11 and W = 6
The width can't be negative, so W = 6 m
L = W + 5
L = 6 + 5
L = 11 m
A = L ∙ W
A = 11 ∙ 6
A = 66 m²
Thank you so much Bosnian!!
To find the length and width of the workbench, we can create an equation using the given information and solve it.
Let's assume the width of the workbench is represented by "x." According to the problem, the length of the workbench is 5 meters greater than the width, so we can represent it as "x + 5."
The area of a rectangle is calculated by multiplying its length by its width. In this case, the area is given as 66 square meters, so we can set up the equation:
x * (x + 5) = 66
Now we have a quadratic equation. Let's solve it step by step:
x^2 + 5x = 66
Rearranging the equation:
x^2 + 5x - 66 = 0
Now we can either factor the quadratic equation or use the quadratic formula. Since the equation is factorable, let's find factors of -66 that add up to 5:
(x + 11)(x - 6) = 0
Setting each factor equal to zero:
x + 11 = 0 or x - 6 = 0
Solving for x:
x = -11 or x = 6
Since dimensions cannot be negative, the width (x) of the workbench is 6 meters. And since the length (x + 5) is 5 meters greater, the length is 6 + 5 = 11 meters.
Therefore, the width of the workbench is 6 meters, and the length is 11 meters.