One side of a rectangle is twice the length of the other. The area is 100. What are the dimensions?

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Answer 1 · 2016-06-10T19:30:49

#color(blue)(=>L=5sqrt(2))" "larr" shorter sides"#

#color(blue)(=>2L=10sqrt(2))" "larr" longer side"#

Let the shorter side length be #L#

Then the longer side length is #2L#

Thus given area #=100=(2L)xx(L)#

#=> 2L^2=100#

Divide both sides by 2 giving

#2/2 L^2=100/2#

But #2/2=1" and "100/2=50#

#L^2=50#

Square root both sides

#sqrt(L^2)=sqrt(50)#

But #" "50" " =" " 10xx5" " =" " 2xx5xx5" " =" " 2xx5^2#

#=>L= sqrt(2xx5^2)#

#color(blue)(=>L=5sqrt(2))" "larr" shorter sides"#

#color(blue)(=>2L=10sqrt(2))" "larr" longer side"#