Question

A custom rectangular tabletop has a length that is twice it’s width, and the tabletop measures 76 inches on its diagonal. What are the dimensions of the tabletop? What is it’s perimeter?

Answer 1

The dimensions of the tabletop: Length= 67.976... inches and Width= 33.988... inches and the perimeter will be 203.929... inches.

Explanation:

Suppose, the width of the rectangular tabletop is
`x` inch.

As the tabletop has a length that is twice it’s width, so the length will be:
`2x` inch.

The tabletop measures 76 inches on its diagonal.

Formula for length of diagonal of rectangle:
`d=√(l^2+w^2)`

So, the equation will be..........

`76=√((2x)^2+ x^2)\\ \\ 76=√(4x^2+x^2) \\ \\ 76=√(5x^2) \\ \\ 5x^2= 76^2= 5776\\ \\ x^2= (5776)/(5)=1155.2 \\ \\ x= √(1155.2) =33.988...`

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.