Question

A photo is printed on an $11$-$inch$ by $13$-$inch$ piece of paper. The photo covers $80squareinches$ and has a uniform border. What is the width of the border?

Answer 1

Find the width of the border:
Given,

• Photo is printed on an $11$-$inch$ by $13$-$inch$ piece of paper.
• The photo covers $80squareinches$ and has a uniform border.

Let the width of the border is $w$.

We know that area of rectangle $=$ length $\times$ width

$$\begin{gathered} \Rightarrow (11-2w)(13-2w)=80 \\ \Rightarrow 143-22w-26w+4w^2=80 \\ \Rightarrow 4w^2-48w+63=0 \end{gathered}$$
We know that roots of equation $a{x}^2+bx+c$ is $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.
$$\begin{gathered} \Rightarrow w=\frac{-(-48)\pm \sqrt{{(-48)}^2-4\times 4\times 63}}{2\times 4} \\ \Rightarrow w=6\pm \frac{\sqrt{1296}}{8} \\ \Rightarrow w=6\pm \frac{36}{8} \\ \Rightarrow w=6\pm 4.5 \end{gathered}$$
$\Rightarrow w=1.5,10.5$

$w=10.5$ cannot be the solution. Thus $w=1.5$

Hence the width of the border is $1.5$-$inch$.