The length of a rectangle is 6 units and its width is 4 units. what is the approximate length of the diagonal of the rectangle? 2 units 4.4 units 6 units 7.2 units

The correct answer is:  [D]:  " 7.2 units" .

Explanation:

Use the Pythagorean theorem:

a² + b² = c² ;

in which:  "6 units" and "4 units" equal the lengths of the right angle (formed by the rectangle);  and "c" is the length of the diagonal of the rectangle, or the "hypotenuse", of the right triangle formed by the rectangle;  We wish to solve for "c" ;


6² + 4² = c² ;  Solve for "c" ;

↔ c² = 6² + 4² ; 

         = (6*6) + (4*4) ;
 
         = 36 + 16 ;

        =  52 ;

    c² = 52 ;

Take the "positive square root" of each side of the equation; to isolate "c" on one side of the equation; and to solve for "c" ; 

  √(c²)  =  √52 ; 

    c = √52 ;  

At this point, we know the 7² = 49 ;  8² = 64 ;  so, the answer is somewhere between "7" and "8" ; yet closer to "7" ;  so among the answer choices given; 

The correct answer is:  [D]:  " 7.2 units" .

However, let use a calculator:

c = √52 = 7.2111025509279786 ; which rounds to "7.2" ;
   which corresponds to:  

Answer choice:  [C]:  " 7.2 units" .

The answer is: y would equal 3 because if you simplify the equation then it would be y= 3x+9 and if you divide 3x and 9 by 3 it would equal 3. y= 3