Answer:
PQ = 46
Step-by-step explanation:
The midsegment ST is half the length of the third side PQ , that is
ST =
PQ , so
5x - 22 =
(3x + 19) ← multiply both sides by 2 to clear the fraction
10x - 44 = 3x + 19 ( subtract 3x from both sides )
7x - 44 = 19 ( add 44 to both sides )
7x = 63 ( divide both sides by 7 )
x = 9
Then
PQ = 3x + 19 = 3(9) + 19 = 27 + 19 = 46
Answer:
The maximum volume is: 11.52 *10.52*2.74 = 332.06 
Step-by-step explanation:
Let x is the side of the square in inches.(x >0)
The volume of the resulting box when the flaps are folded up can be expressed as:
V = x (17 -2x)(16-2x)
= (17x -2
)(16-2x)
=
- 66
+ 272x
To find the value of x which yields the maximum of volume (V), take the first derivative of this equation and set it equal to zero.
= 12
- 66x + 272
Solve 12
- 132x + 272 = 0
<=> x = 2.74
The dimensions of the box are:
Length: (17 -2x) = (17 -2*2.74) = 11.52
Width: (16-2x) = (16-2*2.74) = 10.52
High: x = 2.74
So the maximum volume is: 11.52 *10.52*2.74 = 332.06 