Question

12. (07.06 LC) A library building is in the shape of a rectangle. Its floor has a length of (3x + 5) meters and a width of (5x − 1) meters. The expression below represents the area of the floor of the building in square meters: (3x + 5)(5x − 1) Which of the following simplified expressions represents the area of the floor of the library building in square meters? (5 points) 28x − 5 15x2 − 5 15x2 + 28x − 5 15x2 + 22x − 5

Answer 1

ANSWER

$15 {x}^{2} + 22x - 5$

EXPLANATION

It was given that, the length of the rectangular building is

$(3x + 5) \: meters$

and the width of the is

$(5x - 1) \: meters$

The area of a rectangular building is calculated using the formula for finding the area of a rectangle.

$A = l \times w$

Since the dimensions are given in terms of x, the area is also a function of x,

$A(x) = (3x +5 )(5x - 1)$

We expand to get,

$A(x) = 3x(5x - 1) + 5(5x - 1)$

$A(x) = 15 {x}^{2} - 3x + 25x - 5$

$A(x) = 15 {x}^{2} + 22x - 5$

meters square