Question

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

Answer 1

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

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

Explanation:

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"`