The length of a rectangle is 4 m less than the diagonal and the width is 5 m less than the diagonal. if the area is 82 m^2, how long is the diagonal in meters? round your answers to the nearest tenth.

I hate rounding.

Let's call the diagonal x.  It's the hypotenuse of the right triangle whose legs are the rectangle sides.

According to the problem we have a length x-4 and a width x-5 and an area

82 = (x-4)(x-5)

82 = x^2 - 9x + 20

0 = x^2 - 9x - 62

That one doesn't seem to factor so we go to the quadratic formula

Only the positive value makes any sense for this problem, so we conclude

That's the exact answer.  Did I mention I hate rounding?  That's about

x = 13.6 meters

13.6

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It's not clear to me this problem is consistent.  By the Pythagorean Theorem the diagonal satisfies

which works out to

That's not consistent with the first answer; this problem really has no solution.  Tell your teacher to get better material.

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