Mohammed

Mohammed grew a garden last year. His plot of land was 6 3/4 feet by 10 feet. He wants to have twice as much area and his garden this year. How much area will the new garden take up?

Correct answer:

S₂ =  135 ft²
x =  9.5459 ft
y =  14.1421 ft

Step-by-step explanation:

$$\begin{gathered} a=6{\displaystyle \frac{3}{4}}=6+{\displaystyle \frac{3}{4}}={\displaystyle \frac{6\cdot 4+3}{4}}={\displaystyle \frac{27}{4}}=6.75\text{ ft } \\ b=10\text{ ft } \\ k=2 \\ {S}_1=a\cdot b=6.75\cdot 10={\displaystyle \frac{135}{2}}=67.5{\text{ft}}^2 \\ {S}_2=k\cdot S_1=2\cdot 67.5=135{\text{ft}}^2 \end{gathered}$$

$x=\sqrt{k}\cdot a=\sqrt{2}\cdot 6.75=9.5459\text{ ft}$

$$\begin{gathered} y=\sqrt{k}\cdot b=\sqrt{2}\cdot 10=10\sqrt{2}\doteq 14.1421\text{ ft } \\ \text{ Verifying Solution: } \\ {S}_3=x\cdot y=9.5459\cdot 14.1421=135{\text{ft}}^2 \end{gathered}$$

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