The diagonal of square ABCD is 10. What is the average (arithmetic mean)of the area and the perimeter of the same square?
A.)37.14
B.)13.19
C.)39.14
D.)23.19
A.)37.14
B.)13.19
C.)39.14
D.)23.19
Let x = length of one side of square.datonman wrote:The diagonal of square ABCD is 10. What is the average (arithmetic mean)of the area and the perimeter of the same square?
A.)37.14
B.)13.19
C.)39.14
D.)23.19
The diagonal of square ABCD is 10
So, x² + x² = 10²
Simplify: 2x² = 100
Divide both sides by 2 to get: x² = 50
Solve: x = √50
AREA of square = (side)(side)
= (√50)(√50)
= 50
PERIMETER of square = 4(side)
= 4√50
What is the average (arithmetic mean)of the area and the perimeter of the same square?
Average = (50 + 4√50)/2
NOTE: √49 = 7, so we can see that √50 = a little bit more than 7.
So, 4√50 = a little bit more than 28
So, Average = (50 + a little bit more than 28)/2
= (a little bit more than 78)/2
= a little bit more than 39
= C
Cheers,
Brent
