The hall

The hall had a rectangular ground plan, one dimension 20 m longer than the other. After rebuilding, the length of the hall declined by 5 m, and the width increased by 10 m. The floor area increased by 300 m². What were the original dimensions of the hall?

Correct answer:

a =  50 m
b =  30 m

Step-by-step explanation:

$$\begin{gathered} a=20+b \\ (a-5)(b+10)=ab+300 \\ (a-5)(a-20+10)=a(a-20)+300 \\ (a-5)\cdot (a-10)=a\cdot (a-20)+300 \\ 5a=250 \\ a=\frac{250}{5}=50 \\ a=50=50\text{m} \end{gathered}$$

$b=a-20=50-20=30\text{m}$

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