Arectangle has sides of 4x cm and x cm. the sides of the rectangle are all increased by the same length. if the perimeter of the larger rectangle is 10x + 16, what is the length added to each side, in centimeters?

  4 cm

Step-by-step explanation:

The perimeter of the original rectangle is ...

  P = 2(L+W) = 2(4x + x) = 10x

The perimeter of the larger rectangle after we add "a" to each side is ...

  P = 2(L +W)

  = 2((4x+a) +(x+a))

  = 10x +4a = 10x +16

  4a = 16 . . . . . subtract 10x from both sides

  a = 4 . . . . . . . divide by 4

The length added to each side is 4 cm.

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2

the answer will be