Question

The length of two sides of a right triangle are 5in and 8 in. What is the difference between the two possible length of the third side of the triangle? Round your answer to the nearest tenth

Answer 1

Difference between the two possible lengths of the third side of the triangle=
`3.2` inches

Explanation:

Case 1: For
`\triangle ABC`

Given:

AB=5 in BC=8 in AC= unknown

Using Pythagorean theorem:

`AC^2=AB^2+BC^2`

`AC^2=5^2+8^2` [Plugging in values of
`AB \ and\ BC`

`AC^2=25+64\\AC^2=89`

Taking square root both sides.

`\sqrt AC^2=\sqrt89\\AC=9.43` inches

Case 2: For
`\triangle ABC`

Given:

AC=8 in BC=5 in AB= unknown

Using Pythagorean theorem:

`AB^2=AC^2-BC^2`

`AB^2=8^2-5^2` [Plugging in values of
`AC \ and\ BC`

`AB^2=64-25\\AB^2=39`

Taking square root both sides.

`\sqrt AB^2=\sqrtB9\\AB=6.24` inches

Difference between the two possible lengths of the third side of the triangle=
`9.43-6.24 = 3.19\approx 3.2` inches