Rectangular 44951

The surface area of ​​the rectangular plot needs to be increased by 33.7 percent. One dimension was extended by 2.9 percent. By what percentage should the second dimension be increased? Round the result to two decimal places.

Correct answer:

b =  29.932 %

Step-by-step explanation:

$$\begin{gathered} q=100\%+33.7\%=1+\frac{33.7}{100}=1.337 \\ {p}_1=100\%+2.9\%=1+\frac{2.9}{100}=1.029 \\ S=xy \\ {p}_1\cdot x\cdot p_2\cdot y=q\cdot S \\ {p}_1\cdot p_2\cdot S=q\cdot S \\ {p}_2=q/p_1=1.337/1.029=\frac{191}{147}\doteq 1.2993 \\ {p}_2=1+b/100 \\ b=100\cdot (p_2-1)=100\cdot (1.2993-1)=29.932\% \end{gathered}$$

Try another example