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.
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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`
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