How do i solve this steps and answer please

Length = (x + 8) ft

Step-by-step explanation:

We are given the floor plan of a rectangular room, with the following dimensions:

Area (A) = (x² + 14x + 48) ft²

Width (W) = (x + 6) ft

Length (L) = unknown

We also know that the formula for finding the area of a rectangle is:

A = L × W

We can rearrange the formula to isolate the length by dividing both sides of the equation by W:

Next, we must find the factors of the given area of a rectangle. We can do so by using the factoring by grouping method:

ax² + bx + c   ⇒ (ax² + mx)(nx + c)

a = 1, b = 14, c = 48

In order to do so, we must find factors for "m" and "n," such that:

The product of m × n  = 48, and

The sum of m + n = 14.  

The possible factors that have a product of 48 and a sum of 14 are 6 and 8. Therefore:

m = 6 and n = 8.

= (x² + 6x) + (8x + 48)

Next, factor out x from the first group:

= x(x + 6) + (8x + 48)

Then, factor out 8 from the second group:

= x(x + 6) + 8(x + 6)

Finally, factor out the common term between both groups, (x + 6). Then, combine x + 8:

= x(x + 6) + 8(x + 6)

x² + 14x + 48  = (x + 6)(x + 8)

Now that we have our factors for the given Area of a rectangle, we can proceed with finding the length of the floor plan. Substitute the values into the following formula:

⇒ (x + 6) cancels out, leaving us with (x + 8):

L = x + 8

Area (A) = (x² + 14x + 48) ft²

Width (W) = (x + 6) ft

Length (L) = (x + 8) ft

In order to verify whether we have the correct value for the length, substitute its value into the formula for finding the area of a rectangle:

A = L × W

x² + 14x + 48 = (x + 8)(x + 6)

Perform the FOIL method on the right-hand side of the equation:

x² + 14x + 48  =  x² + 6x + 8x + 48

Combine like terms on the right-hand side:

x² + 14x + 48  =  x² + 14x + 48    ⇒ True statement.

Therefore, the length of the floor plan is (x + 8) ft.

Step-by-step explanation: