The lengths of two sides of a right triangle are 12 inches and 15 inches. what is the difference between the two possible
lengths of the third side of the triangle? round your answer to the nearest tenth.
10.2 inches
24.0 inches
28.2 inches
30.0 inches

The correct option is A

Step-by-step explanation:

Lets suppose that the third side is hypotenuse.

We will apply Pythagorean theorem:

c²= a²+b²

where,

a=12 inches

b=15 inches

Now substitute the values in the theorem:

c²=(12)²+(15)²

c²=144+225

c²=369

Take square root on both sides:

√c²=√369

c= 19.2 inches.

Now assume that the third side is a leg:

Here we will find the value of b.

a=12 inches

c= 15 inches.

b= ?

Now substitute the values in the theorem:

c²=a²+b²

(15)²=(12)²+b²

225=144+b²

Move the constant to the L.H.S

225-144=b²

81=b²

Take square root on both sides:

√81=√b²

9=b

Now we will find the difference of the third sides:

19.2-9 = 10.2

Thus the length of the third side is 10.2 inches

The correct option is A

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation: