Question

Mike and Ryan are playing in a rectangular swimming pool. They are at opposite corners of the pool, as shown in the following illustration.The length of the swimming pool is 12 feet, and the width is t feet less than the length. Which of the following equations can be used to calculate the values of t for which the distance between Mike and Ryan is 32 feet?

Answer 1

the question does not present the options, but this does not interfere with the resolution

Let

x------> the length of the swimming pool

y------> the width of the swimming pool

we know that

x=12 ft

y=12-t

the distance between Mike and Ryan is equal to the distance of the diagonal of the rectangular swimming pool
D is the diagonal
D=32 ft-----> D²=32²----> equation 1
D²=x²+y²---> D²=12²+(12-t)²-----> equation 2

equate equation 1 and equation 2
32²=12²+(12-t)²------> 1024=144+(144-24t+t²)

t²-24t-736=0-----> this equation can be used to calculate the values of t 

the answer is

the equation t²-24t-736=0 

can be used to calculate the values of t 

Answer 2

\sqrt((12)^(2)+(12-t)^(2))=32