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:

$$\begin{gathered} a=6\frac{3}{4}=6+\frac{3}{4}=\frac{6\cdot 4+3}{4}=\frac{24+3}{4}=\frac{27}{4}=6.75\text{ft} \\ b=10\text{ft} \\ k=2 \\ {S}_1=a\cdot b=\frac{27}{4}\cdot 10=\frac{27\cdot 10}{4}=\frac{270}{4}=\frac{135}{2}=67.5{\text{ft}}^2 \\ {S}_2=k\cdot S_1=2\cdot \frac{135}{2}=\frac{2\cdot 135}{2}=\frac{270}{2}=135{\text{ft}}^2 \end{gathered}$$

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

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

Try another example