Question

Your building a patio area along two sides of a pool. The pool is rectangular with a width of 50 feet and a length of 100 feet. The patio area will have the same width on each side of the pool. Write a polynomial that represents the combined area?

Answer 1

`x^2+150x`

Explanation:

The drawing above represents the pool in blue, and the patio in brown and black.

We need to find out the area of the two brown areas (A and B) plus the black area.

Rectangle A has a long side of length `100` (same as the pool) and a short side of length `x`, giving us an area of `100x` ft.

Rectangle B has a long side of `50` and a short side of `x`, giving us the area of `50x` ft

The black area is a square as it has `x` for both of its sides, so its area is `x^2` ft

Now we just add all three to get the final equation:
`x^2+100x+50x`

OR

`x^2+150x`