Question

A rectangular painting has an area of (2x^2 + 8x + 6) cm^2 . Its length is (2x + 2) cm. Find the width of the painting.

Answer 1

Width = x + 3

Explanation:

The formula for the area of a rectangle is: A = LW, where A=area, L = length and W = width. In order to get the expression for the value of the width, you first need to factor each equation given for both the area and the length. Starting with the length (2x + 2), you can factor out the 2 to get: 2(x+1). With the area: 2x² + 8x + 6, you can first factor out the 2 to get: 2(x² + 4x + 3). Next, you can factor the polynomial: 2(x + 3)(x + 1). Lastly, in order to find the width, you divide the area by the length:

`(2(x + 3)(x + 1))/(2(x+1))`

Crossing out the common terms from the numerator and denominator, '2' and '(x + 1)', we get a final answer of W = x + 3.