Find the dimensions of rectangle with given area and ratio of sides

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I have memorized this question and I couldn't really get how I could figure it out. The question asks:

Its length is 5 times twice its width
The area is 7 square meters
Find the dimensions of this rectangle

I know its $l \times w \times h$... I don't know how I could use factoring to solve this.

Should I use gfc? Which factoring should I use? Please give me hints so I can figure out how to do this

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1 Answer

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The area formula of a rectangle with sides $a$ and $b$ is $A=ab$. If $a$ is the width, the text says $$\underbrace{b}_{\text{length}} = \underbrace{5\cdot}_{\text{5 times}}\ \underbrace{2\cdot}_{\text{twice}}\ \underbrace{a}_{\text{its width}} = 10a$$ also the text says $A = 7$. Now solve $$7 [m^2]=A=ab=a\cdot (10 a) = 10 a^2$$ for $a$ and substitute into $b=10a$ to get the dimensions of the rectangle. Note that $a$ and $b$ will be in $m$ (meters).

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