Rectangular 80436

The longer dimension of the rectangular plot was reduced by one-fifth, and the shorter dimension by 8%. By what percentage did the amount of land decrease? What is the perimeter of the fence now if the original dimensions of the fence were 60m and 25m?

Correct answer:

p =  26.4 %
o₂ =  142 m

Step-by-step explanation:

$$\begin{gathered} a=60\text{m} \\ b=25\text{m} \\ r=100\%-8\%=1-\frac{8}{100}=0.92 \\ x=a-a/5=60-60/5=48\text{m} \\ y=b\cdot r=25\cdot 0.92=23\text{m} \\ {S}_1=a\cdot b=60\cdot 25=1500{\text{m}}^2 \\ {S}_2=x\cdot y=48\cdot 23=1104{\text{m}}^2 \\ p=100\cdot \frac{S_1-S_2}{S_1}=100\cdot \frac{1500-1104}{1500}=26.4\% \end{gathered}$$

$o_2=2\cdot (x+y)=2\cdot (48+23)=142\text{m}$

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