An oriental rug is 5 feet longer than it is wide. if the diagonal of the rug is 12 feet, find its dimensions to the nearest tenth of a foot.

Step-by-step explanation:

Let be:

 "l" the lenght in feet of the oriental rug.

"w" the width in feet of the oriental rug.

"d" the length of the diagonal (in feet) of the oriental rug.

According to the exercise:

By definition, the diagonal of a rectangle can be calculated with the Pythagorean Theorem. Then, we can say that:

Now, we must substitute the equation   and the value of "d" into and then we must solve for "w":

Applying the Quadratic formula . we get:

The width of the rug is the positive value:

Finally, you can substitute the width into to find the length:

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

hope this .

r3t40