Question

HELP ASAP TAKING A TEST I DONT KNOW HOW TO DO THESE I HAVE 1 HOUR PLEASE!

Answer 1

diagonal is 11.14 cm

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:

`L=(4+/-√(4^2-4(1)(-31)) )/(2) \\L=(4+/-√(140) )/(2)\\L=7.916\\or\\L=-3.916`

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:

`diag=√(7.916^2+7.832^2)\approx11.1356\,\,cm`

which rounded to two decimal places is 11.14 cm