Question

The dimensions of a window are 5x+5 and 2x+6. What is the area of the window?

Answer 1

Our answer is 10x^2 + 40x + 30.

`\Large\texttt{Explanation}`

We are asked to find the area of a window, given that:

• its length is 5x + 5
• its width is 2x + 6

The formula for a rectangle's area (assuming the window is a rectangle) is A = LW, where A = area, L = length, and W = width.

Substitute the values:

`\multimap\qquad\bf{A=(5x+5)(2x+6)}`

To multiply these binomials, use FOIL (first, outside, inside, last):

`\multimap\qquad\bf{A=5x*2x+5x*6+5*2x+5*6}`

`\multimap\qquad\bf{A=10x^2+30x+10x+30}`

`\multimap\qquad\boxed{\bf{A=10x^2+40x+30}}`

`\therefore` the area is 10x^2 + 40x + 30.

Answer 2

`\sf \textsf{Area of the window} = 10x^2 + 40x + 30`

Explanation:

To find the area of the window, we need to multiply its length and width.

The dimensions of the window are given as
`\sf 5x + 5` and
`\sf 2x + 6`.

The area (
`\sf A`) is given by:

`\sf A = \text{Length} * \text{Width}`

Substitute the given expressions for length and width:

`\sf A = (5x + 5) * (2x + 6)`

Now, use the distributive property to multiply:

`\sf A = 5x * (2x + 6) + 5 * (2x + 6)`

`\sf A = 10x^2 + 30x + 10x + 30`

Combine like terms:

`\sf A = 10x^2 + 40x + 30`

So, the area of the window is
`\sf 10x^2 + 40x + 30`.