A picture frame, 5 cm wide, has a length which is twice the width, x cm.
a) Find an expression for the total area of the frame and picture.
b) Find an expression in expanded form for the area of picture only.
We know that the breadth (width) of the outside edge of the picture (ie including the frame) = x cm.
`therefore b=x `
As the length is twice the outside breadth (width), we know that `l=2 times b`
And we know that the area of a rectangle is `l times b`
`therefore A=2x times x`
`therefore = 2x^2`
For the picture only, we know that the frame is 5cm in width and we must deduct 5 cm from each side to find the length and breadth (width) of the picture itself (without the frame).
`therefore l= 2x-10 and b=x-10`
`= 2x^2-30x +100`
The total area of the outside edge of the picture and frame is `2x^2`
and the expression representing the area of the picture only is `2x^2-30x+100`