Answer:
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:
[tex]L=\frac{4+/-\sqrt{4^2-4(1)(-31)} }{2} \\L=\frac{4+/-\sqrt{140} }{2}\\L=7.916\\or\\L=-3.916[/tex]
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:
[tex]diag=\sqrt{7.916^2+7.832^2}\approx11.1356\,\,cm[/tex]
which rounded to two decimal places is 11.14 cm
