The longest side of an obtuse triangle measures 20 cm. the two shorter sides measure x cm and 3x cm. rounded to the nearest tenth, what is the greatest possible value of x? 6.3 6.4 7.0 7.1

the sum of the lengths of any two sides of a triangle is greater than the length of the third side (triangle inequality theorem)

case a) 

case b)       

case c) 

therefore

the answer is

6.4 cm

the greatest possible value of x is:

6.3

step-by-step explanation:

we apply the pythagorean theorem for obtuse triangle:

a² + b² < c²

where c denotes the longest side of the triangle.

a = x ; b = 3x ; c = 20  

⇒   x² + (3x)² < 20²

⇒   x² + 9x² < 400

⇒   10x² < 400

⇒   x² < 400 / 10   (on dividing both side of the inequality by 10)

⇒   x² < 40

⇒   √x² < √40   (on taking square root on both the sides of the inequality)

⇒   x < 6.32

hence, the greatest possible value of x is:

6.3

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