Rectangle's dimensions

The rectangle has an area of 147 cm². One of its sides is three times longer than the other side. We increase the shorter side of the rectangle by 8 cm. By how many cm² will the new rectangle's area be larger than the original rectangle?

Final Answer:

x =  168 cm²

Step-by-step explanation:

$$\begin{gathered} S=147{\text{cm}}^2 \\ a=3b \\ S=ab=3b^2 \\ b=\sqrt{S/3}=\sqrt{147/3}=7\text{cm} \\ a=3\cdot b=3\cdot 7=21 \\ {S}_1=a\cdot (b+8)=21\cdot (7+8)=315{\text{cm}}^2 \\ x=S_1-S=315-147=168{\text{cm}}^2 \end{gathered}$$

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