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    i need help

    How can the surface area of a rectangular prism change if evey one of the dimensions is increased by a factor of x? and how can we prove that?
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    Quote Originally Posted by rose1 View Post
    How can the surface area of a rectangular prism change if evey one of the dimensions is increased by a factor of x? and how can we prove that?
    Take any rectangular prism. Let the lengths of the sides (width, height, and length) be $\displaystyle u,\,v,$ and $\displaystyle w.$ Then what is the surface area of this prism? It is just the sum of the areas of each face:

    $\displaystyle S=2uv+2vw+2uw.$

    If you increase each dimension by a factor of $\displaystyle x$, then the new dimensions are $\displaystyle ux,\,vx,$ and $\displaystyle wx.$ So what will the new surface area be? Now compare this to that of the original.
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