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 $" "50" " =" " 10xx5" " =" " 2xx5xx5" " =" " 2xx5^2$

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

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

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