Question

A right triangle has side lengths 4 units, 5 units, and x units. It is unknown if the missing length is the longest or shortest side. Rounded to the nearest tenth, what is the difference between the possible values of x? 3.0 units 3.4 units 6.4 units 8.0 units

Answer 1

When x is longest then x is 6.4 units and when x is shortest then x =3 units

Explanation:

Given a right triangle has side lengths 4 units, 5 units, and x units. Also, it is given that missing length is the longest or shortest side.

∴ Two cases formed

Case 1: When missing length is longest side i.e when x is longest.

By Pythagoras theorem,

x² = a² + b²

where a and b are other two sides which are given 4 units and 5 units.

∴ x² = 4² + 5²

= 16+25= 41

x = √41=6.4 units

Case 2: When missing length is longest side i.e when x is the shortest:

x² = 5²-4²

= 25-16=9

x =√9=3 units

Difference = 6.4 - 3= 3.4 units

Answer 2

3.4 units

Explanation

The lengths of a triangle are; 2 units, 5 units and x units. These 3 are connected by a formula of Pythagoras theorem.

c² = a² + b²

Where c is the longest side, a and b are the legs of the rectangle.

When x is the longest:

∴ x² = 4² + 5²

= 16 + 25

= 41

x = √41

= 6.4 units

When x is the shortest:

x² = 5² - 4²

= 25 - 16

= 9

x = √9

= 3 units

Difference = 6.4 - 3

= 3.4 units