Answer:
1. 16 ft
[tex]\sf 2.\quad \dfrac{29}{99}[/tex]
Step-by-step explanation:
Question 1
Formula
Area of a square = s² (where s is the side length)
Given:
Substitute the given area into the formula and solve for s:
[tex]\sf \implies 256=s^2[/tex]
[tex]\sf \implies \sqrt{256}=\sqrt{s^2}[/tex]
[tex]\sf \implies s=\pm 16[/tex]
As distance is positive, the length of one side of Keisha's kitchen is 16 ft.
Question 2
Converting a recurring decimal to a fraction
Let x equal the recurring decimal:
[tex]\implies \sf x=0.292929...[/tex]
Create another number with recurring 29s by multiplying the above by 100:
[tex]\implies \sf 100x=29.292929...[/tex]
To solve these two equations and write x as a fraction, subtract the first equation from the second to remove all the recurring digits after the decimal point:
[tex]\begin{array}{r r c l}& \sf 100x &= &\sf 29.292929...\\- & \sf x&=& \sf \phantom{..}0.292929...\\\cline{1-4} & \sf 99x&=& \sf29\\\cline{1-4}\end{array}[/tex]
Therefore:
[tex]\implies \sf 99x=29[/tex]
[tex]\implies \sf x=\dfrac{29}{99}[/tex]
Therefore:
[tex]\sf \implies 0.\overline{29}=\dfrac{29}{99}[/tex]
Learn more about converting recurring decimals to fractions here:
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