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

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 $x$ 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:  $d=\sqrt{l^2+w^2}$

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

$76=\sqrt{(2x)^2+ x^2}\\ \\ 76=\sqrt{4x^2+x^2} \\ \\ 76=\sqrt{5x^2} \\ \\ 5x^2= 76^2= 5776\\ \\ x^2= \frac{5776}{5}=1155.2 \\ \\ x= \sqrt{1155.2} =33.988...$

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.