Respuesta :
Answer:
Width: 10.5 feet
Length: 31.5 feet
Step-by-step explanation:
Let x represent width of the concrete slab.
We have been given that the length of a concrete slab is three more than three times the width. So length of the slab would be [tex]3x[/tex].
We are also told that the area of slab is 330 square feet. We can represent this information in an equation as:
[tex]x\cdot 3x=330[/tex]
[tex]3x^2=330[/tex]
[tex]x^2=\frac{330}{3}[/tex]
[tex]x^2=110[/tex]
Now, we will take square root of both sides.
[tex]\sqrt{x^2}=\sqrt{110}[/tex]
[tex]x=10.488\approx 10.5[/tex]
Therefore, the width of slab is approximately 10.5 feet.
The length of the slab would be [tex]3x\Rightarrow3(10.5)=31.5[/tex].
Therefore, the length of slab is approximately 31.5 feet.
Answer: the length of the longer side of the slab is 33 feet
Step-by-step explanation:
Let L represent the length(longer side) of the concrete slab.
Let W represent the width(shorter side) of the concrete slab.
The length of a concrete slab is three more than three times the width. This would be expressed as
L = 3W + 3
The formula for determining the area of a rectangle is expressed as
Area = Length × Width
It's area is 330 square feet. This means that
LW = 330 - - - - - - - - - - -1
Substituting L = 3W + 3 into equation 1, it becomes
W(3W + 3) = 330
3W² + 3W = 330
3W² + 3W - 330 = 0
Dividing through by 3, it becomes
W² + W - 110 = 0
W² + 11W - 10W - 110 = 0
W(W + 11) - 10(W + 11) = 0
W - 10 = 0 or W + 11 = 0
W = 10 or W = - 11
Since the width cannot be negative, then W = 10
L = 3W + 3 = (3 × 10) + 3
L = 30 + 3 = 33
