Question

The length of a concrete slab is three more than three times the width. It's area is 330 square feet. What is the length of the longer side of the slab?

Answer 1

Answer: the length of the longer side of the slab is 33 feet

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

Answer 2

Width: 10.5 feet

Length: 31.5 feet

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
`3x`.

We are also told that the area of slab is 330 square feet. We can represent this information in an equation as:

`x\cdot 3x=330`

`3x^2=330`

`x^2=(330)/(3)`

`x^2=110`

Now, we will take square root of both sides.

`√(x^2)=√(110)`

`x=10.488\approx 10.5`

Therefore, the width of slab is approximately 10.5 feet.

The length of the slab would be
`3x\Rightarrow3(10.5)=31.5`.

Therefore, the length of slab is approximately 31.5 feet.