The lengths of two sides of a right triangle are 5 inches and 8 inches. what is the difference between the two possible
lengths of the third side of the triangle? round your answer to the nearest tenth.
3.1 inches
3.2 inches
10.0 inches
15.7 inches

Option 2 - 3.2 inches.                      

Step-by-step explanation:

We have given that the lengths of two sides of a right triangle are 5 inches and 8 inches.

We have to find what is the difference between the two possible  lengths of the third side of the triangle?

Solution :

The lengths of two sides of a right triangle are 5 inches and 8 inches.

Applying Pythagoras theorem,

Where, z is the hypotenuse the longer side of the triangle

x is the perpendicular

y is the base are the shorter side of the triangle

We have assume that z=8 inches and y = 5 inches

Substitute the value in the formula,

We have assume that x=8 inches and y = 5 inches

Substitute the value in the formula,

Therefore, The possible length of the third side of the triangle is

Therefore, The difference between the two possible  lengths of the third side of the triangle is 3.2 inches.

Hence, Option 2 is correct.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: