Let r be a rectangle The ratio of the lengths of the height

Let r be a rectangle. The ratio of the lengths of the height to width of r is radical 5. The diagonal of r has length 6. Then the area of r is

Radical 5

6 radical 5

5

Solution

Let the height be xsqrt5

and width be x

diagonal=sqrt(5x^2+x^2)=x sqrt6

xsqrt6=6

x=sqrt6

height=sqrt30

width=sqrt6

area=sqrt30*sqrt6=sqrt180=6sqrt5 or 6 radical 5