Question

The shorest side of a triangle has a length of 14 the other sides have a lengths x+1 and x+3 find the value of x that makes the triangle a right triangle

A. 188
B.47
c.23
D.1

Answer 1

x = 47

Explanation:

The equation for the sides of a right triangle is also call the Pythagorean Theorem: a² + b² = c²

Given that 14 is the shortest side, then (x +1) is likely the other side and (x +3) is the hypotenuse. We can then plug this value and expressions into our equation: 14² + (x + 1)² = (x+3)² or 196 + (x + 1)(x + 1) = (x + 3)(x +3).

Distribute: 196 + x² + 2x + 1 = x² + 6x + 9

Combine like terms: 188 = 4x

Divide: x = 47

Check: 14² + 48² = 50² or 196 + 2304 = 2500 or 2500 = 2500