Question

Inside that rectangle, there is a smaller one. It has a width of 2x and a length of x + 12. How do you find the area?

Answer 1

`2x^2+24`

Explanation:

Recall that the formula for area of a rectangle is:

`color(blue)(|bar(ul(color(white)(a/a)A=lwcolor(white)(a/a)|)))`

where:
`A=`area of rectangle
`l=`length
`w=`width

To determine the area of the rectangle, substitute the given expressions for the length and width into the formula for the area of a rectangle.

`A=lw`

`A=(color(darkorange)x+color(blue)(12))(color(red)(2x))`

Use the distributive property, `color(red)a(color(darkorange)b+color(blue)c)=color(red)acolor(darkorange)b+color(red)acolor(blue)c`, to simplify the equation.

`A=(color(red)(2x))(color(orange)x)+(color(red)(2x))(color(blue)12)`

`A=color(green)(|bar(ul(color(white)(a/a)2x^2+24xcolor(white)(a/a)|)))`