Jose unlocks his cellphone by placing his right thumb on a square of 1 centimeter by 1 centimeter at the center of the screen. Upon recognizing his thumbprint, the square expands outward. The cellphone unlocks when the perimeter reaches 32 centimeters, taking a total of 2.5 seconds. What is the perimeter of the square after 1.5 seconds? How is the answer 20.8?

20.8 cm

Step-by-step explanation:

Perimeter of square = 4a

Dimension of the thumb print = 1 cm by 1cm

Perimeter of the size of the square (thumb print) = 4 × 1

= 4 cm

We are told in the question that:

The cellphone unlocks when the perimeter reaches 32 centimeters, taking a total of 2.5 seconds.

Hence,

32cm - 4cm = 28cm

What is the perimeter of the square after 1.5 seconds?

We set up a proportion

Time / perimeter

= 1.5/x = 2.5/ 28

Cross Multiply

= 2.5x = 1.5 × 28

x = 1.5 × 28/2.5

x = 16.8.

Therefore, the perimeter of the square after 1.5 seconds

= 16.8cm + perimeter of the square before expansion.

=16.8 cm + 4 cm

= 20.8 cm