Question

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

Answer 1

Answer: B. 3.2 inches

Step-by-step explanation: I took the test and i got it right

Answer 2

Option 2 - 3.2 inches.

Explanation:

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

To find : What is the difference between the two possible lengths of the third side of the triangle?

Solution :

According to question, it is a right angle triangle

Applying Pythagoras theorem,

`H^2=P^2+B^2`

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

P is the perpendicular

B is the base

Assume that H=8 inches and B = 5 inches

Substitute the value in the formula,

`8^2=P^2+5^2`

`64=P^2+25`

`P^2=64-25`

`P^2=39`

`P=√(39)`

`P=6.24`

Assume that P=8 inches and B = 5 inches

Substitute the value in the formula,

`H^2=8^2+5^2`

`H^2=64+25`

`H^2=89`

`H=√(89)`

`H=9.43`

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

`L=H-P`

`L=9.43-6.24`

`L=3.19`

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

So, Option 2 is correct.