I have a rectangle with a known area and a known ratio of length/width. How do I calculate the length and width.
Area: 1500 sq ft Ratio: 241 / 625 = .386
How do I calculate the length and width in feet.
$\endgroup$ 22 Answers
$\begingroup$Let the length of the rectangle be $l $ and the width be $w$. We know the area of the rectangle is $A = lw \tag {1}$.
Now it is given that $\frac {l}{w} = \frac {241}{625} \Rightarrow l = \frac {241}{625}w \tag {2}$.
Now substituting $(2)$ in $(1)$, we have, $$A = \frac {241}{625}w^2 =1500$$ $$w = \sqrt {\frac {1500\times 625}{241}} = \frac {10\times 25\times \sqrt {15}}{\sqrt {241}} = \frac {250\sqrt {15}}{\sqrt {241}} $$
Now I leave it to you to find $l$ using $(2)$. Hope it helps.
$\endgroup$ 2 $\begingroup$Hint:
Area$=$ length $\times$ width,
and
length$=\frac{241}{625}$ width,
so:
Area$= \frac{241}{625}$ width $\times$ width $= \frac{241}{625} x^2=1500$
Can you solve for $x$?
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