A student 5

A student took the measurements of his classroom and gave the width as 7m and the length as 9m. If there is an error of 2 percent in measurement, determine the greatest value of [X+Y]/X if X and Y are the width and length of the classroom, respectively. Give your answer to 4 decimal places.

Correct answer:

w =  2.3319

Step-by-step explanation:

$$\begin{gathered} a=7\text{m} \\ b=9\text{m} \\ e=2\%=\frac{2}{100}=\frac{1}{50}=0.02 \\ {e}_1=1+e/2=1+0.02/2=\frac{101}{100}=1\frac{1}{100}=1.01 \\ {e}_2=1-e/2=1-0.02/2=\frac{99}{100}=0.99 \\ {w}_0=\frac{a+b}{a}=\frac{7+9}{7}=\frac{16}{7}=2\frac{2}{7}\doteq 2.2857 \\ w=\frac{a\cdot e_1+b\cdot e_1}{a\cdot e_2}=\frac{7\cdot 1.01+9\cdot 1.01}{7\cdot 0.99}=2.3319 \end{gathered}$$

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