The length of a rectangular swimming pool is 2x-1 meters and the width is x+2 meters. Write a polynomial A(x) that represents the area. Find A(5).
Isn't Area of a rectangle = length x width ?
so ..
A(x) = (2x-1)(x+2)
evaluate A(5)
To find the polynomial A(x) that represents the area of the rectangular swimming pool, we need to multiply the length and width of the swimming pool.
The length is given as 2x-1 meters, and the width is given as x+2 meters.
So, the area A(x) can be found by multiplying the length by the width:
A(x) = (2x-1)(x+2)
Now, let's expand the expression:
A(x) = 2x(x+2) - 1(x+2)
A(x) = 2x^2 + 4x - x - 2
Simplifying further, we get:
A(x) = 2x^2 + 3x - 2
To find A(5), we substitute x = 5 into the polynomial:
A(5) = 2(5)^2 + 3(5) - 2
A(5) = 2 * 25 + 15 - 2
A(5) = 50 + 15 - 2
A(5) = 63
Therefore, A(5) = 63 square meters, which represents the area of the rectangular swimming pool.