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diagonal is 11.14 cm

Step-by-step explanation:

We start by writing the equation for the width (w) in terms of the length (L):

w = 2 L - 8

from the area = w * L = 62

we replace w in it:    w * L = (2 L -8) * L = 62

2 L^2 - 8 L = 62

2 L^2 - 8 L - 62 = 0

extract 2 common factor:

2 (L^2 - 4 L - 31) = 0

Using quadratic formula we get:

So, we pick the positive answer L = 7.916 cm

Then we now know the with of the rectangle as well:

w = 2 * L - 8 = 2 * 7.916 - 8 = 7.832  cm

Now we estimate the diagonal of the rectangle using the Pythagorean theorem:

which rounded to two decimal places is 11.14 cm

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step-by-step explanation: