A picture frame measures $14$ cm by $20$ cm. $160$ cm$^2$ of the picture shows inside the frame. Find the width of the frame.

You know what a picture frame looks like, right? Two concentric rectangles.

You are given the dimensions of the outer rectangle. You are given the area of the inner rectangle.

You are asked to find the thickness of the border between them.

$$20\textrm{cm}\left\{ \vphantom{\bbox[green, 2ex, border:solid 1pt]{\bbox[white, 1ex, border:solid 1pt]{\begin{array}{l}\qquad\\160\textrm{cm}^2\\~\\~\end{array}}}} \right. % \overbrace{\bbox[green, 2ex, border:solid 1pt]{\bbox[white, 1ex, border:solid 1pt]{\begin{array}{l}\qquad\\160\textrm{cm}^2\\~\\~\end{array}}}}^{14\textrm{cm}}$$


You are expected to assume that the picture frame has a constant width. That width creates a border around the picture. Note that the area of the frame is $280 \text{ cm}^2$, which is larger than the picture. You are supposed to find th width of the frame.


The question pretty ambiguous. My interpretation would be that you have a rectangular picture frame whose exterior dimensions are $14\times 20$. The frame has uniform width, so all sides are the same width. If you place a picture in the frame then $160$ square cm of the picture will be visible. What is the width of a side of the frame?

Tags:

Geometry

Algebra Precalculus

Geometric Interpretation

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