The length 20

The length and breadth of a rectangular park are in the ratio 8:5. A path,1.5 m wide, running all around the outside of the park has an area of 594 sq m. Find the dimensions of the park.

Correct answer:

a =  120 m
b =  75 m

Step-by-step explanation:

$$\begin{gathered} a:b=8:5=8x+5x \\ p=2\cdot 1.5=3\text{m} \\ {A}_2=594{\text{m}}^2 \\ (8x+p)\cdot (5x+p)=8x\cdot 5x+A_2 \\ (8x+3)\cdot (5x+3)=8x\cdot 5x+594 \\ (8\cdot x+3)\cdot (5\cdot x+3)=8\cdot x\cdot 5\cdot x+594 \\ 39x=585 \\ x=\frac{585}{39}=15 \\ x=15 \\ a=8\cdot x=8\cdot 15=120\text{m} \end{gathered}$$

$b=5\cdot x=5\cdot 15=75\text{m}$

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