Given :
Area of rectangle = 490 units²
length = 8x
width = 5x
As we know
[tex]\:\bf\boxed{{Area\:of\:rectangle\:=\:length\:}x\:{width}}[/tex]
So,
Area of rectangle = l x w
=> 490 units² = [tex]\:\mathsf{8x\: x\: 5x}[/tex]
=> 490 = [tex]\:\mathsf{40x²}[/tex]
=> [tex]\:\mathsf{\frac{490}{40}}[/tex] = x²
=> x² = [tex]\:\mathsf{\frac{49}{4}}[/tex]
=> x = [tex]\:\mathsf{\sqrt{\frac{49}{4}}}[/tex]
=> x = [tex]\:\mathsf{\frac{7}{2}}[/tex]
=> x = [tex]\:\mathsf{3.5}[/tex]
Now,
length = 8x = 8 x 3.5 = 28 units
width = 5x = 5 x 3.5 = 17.5 units
Therefore the required length and width of the rectangle are 28 units and 17.5 units.
Hope this helps!
