Rectangle area

The length of a rectangle of x units is increased by 10% and its width of y units is increased by 15%. What is the ratio of the area of the old rectangle to the area if the new rectangle?

Correct result:

r =  1.265
p =  26.5 %

Solution:

$a_{2}=1.10 \ a_{1} \ \\ b_{2}=1.15 \ b_{1} \ \\ S_{1}=a_{1} \cdot \ b_{1} \ \\ S_{2}=a_{2} \cdot \ b_{2}=1.10 \ a_{1} \cdot \ 1.15 \ b_{1} \ \\ S_{2}=1.10 \cdot \ 1.15 \cdot \ S_{1} \ \\ r=1.10 \cdot \ 1.15=\dfrac{ 253 }{ 200 }=1.265$
$p=100 \cdot \ (r - 1)=100 \cdot \ (1.265 - 1)=\dfrac{ 53 }{ 2 }=26.5 \%$

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