Rectangle Square Area Difference

In the given rectangle, the length is 12 m greater than the width. We get a square if we reduce the length by 10 m and increase the width by 2 m. The area of the original rectangle is 300 m² more than the area of the square. Determine the dimensions of the rectangle.

Final Answer:

a =  50 m
b =  38 m

Step-by-step explanation:

$$\begin{gathered} a=12+b \\ a-10=2+b \\ a\cdot b=(a-10)\cdot (2+b)+300 \\ a\cdot (a-12)=(a-10)\cdot (2+(a-12))+300 \\ 8a=400 \\ 8\cdot a=400 \\ 8a=400 \\ a=\frac{400}{8}=50 \\ a=50=50\text{m} \end{gathered}$$

$$\begin{gathered} b=a-12=50-12=38=38\text{m} \\ {S}_1=a\cdot b=50\cdot 38=1900{\text{m}}^2 \\ {S}_2=(a-10)\cdot (2+b)=(50-10)\cdot (2+38)=1600{\text{m}}^2 \\ {S}_3=S_1-S_2=1900-1600=300{\text{m}}^2 \end{gathered}$$

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