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

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

step-by-step explanation:

there are 36 inches in a yard

25 : 36 = 0.69 yards (you can round to 0.70)