Question

You are building a brick patio. The length of the patio is (x + 11) feet. The total area of the patiocan be represented by x^2 + 14x + 33. The area of the patio is 240 square feet. Find the lengthof the patio in feet.

Answer 1

20 ft

Step-by-step explanation:

The total area of the patio is represented by x² + 14x + 33 and it is also equal to 240. So, we can write the following equation:

x² + 14x + 33 = 240

Now, we can subtract 240 from both sides:

x² + 14x + 33 - 240 = 240 - 240

x² + 14x - 207 = 0

So, to factorize the expression, we need to find two numbers that sum to 14 and multiply to -207. These numbers are -9 and 23, so:

(x - 9)(x + 23) = 0

Then, we get that the solutions for x are:

x - 9 = 0

x - 9 + 9 = 0 + 9

x = 9

or

x + 23 = 0

x + 23 - 23 = 0 - 23

x = -23

Since x = -23 doesn't have a sense here, the value for x is 9.

Finally, with the value of x = 9, we can calculate the length of the patio as:

Length = x + 11

Length = 9 + 11

Length = 20 ft

So, the length of the patio is 20 ft.