Answer:
The dimensions of the tabletop: Length= 67.976... inches and Width= 33.988... inches and the perimeter will be 203.929... inches.
Step-by-step explanation:
Suppose, the width of the rectangular tabletop is [tex]x[/tex] inch.
As the tabletop has a length that is twice it’s width, so the length will be: [tex]2x[/tex] inch.
The tabletop measures 76 inches on its diagonal.
Formula for length of diagonal of rectangle: [tex]d=\sqrt{l^2+w^2}[/tex]
So, the equation will be..........
[tex]76=\sqrt{(2x)^2+ x^2}\\ \\ 76=\sqrt{4x^2+x^2} \\ \\ 76=\sqrt{5x^2} \\ \\ 5x^2= 76^2= 5776\\ \\ x^2= \frac{5776}{5}=1155.2 \\ \\ x= \sqrt{1155.2} =33.988...[/tex]
Thus, the width of the tabletop is 33.988... inches and the length will be: (2×33.988...) = 67.976... inches.
The perimeter will be: 2(33.988...+ 67.976...) inches = 203.929... inches.