The height is: 10.61 units.Â
            {or, write as:  "(7.5 √2)  units"}.Â
Explanation:
Area of a triangle:Â A = 1/2 * base * height = 1/2 * b * h ;
Given: Â b = 1.5 * h ;
      A = 75 units²
Solve for "h" ("height") ; Â h = 1.5 b ;
So, we solve for "b" ; then we plug that value into the equation:Â
 Â
    →  h = 1.5 b ;  to get the height, "h" ;
    →  75 = 1/2 * (b) (1.5 b) ;
     Multiply the ENTIRE equation by "2" ;
 to get rid of the fraction and decimals ;Â
    →  2 * { 75 = 1/2 * (b) (1.5 b) } ;
    →  150 =  b * 3b ;
    →  150  =  3 b²  ; Â
Â
    ↔ 3 b² =  150 ;Â
Â
      Now, divide EACH side of the equation by "3" ;
    →  3 b² / 3 = 150 / 3 ;Â
    →   b²  = 50 ;
      Now, take the POSITIVE square root of each side of the equation;
to isolate "b" on one side of the equation; and to solve for "b" ;
     →  √(b²)  =  √50
     →    b  =  √50
    →   √50 = √25 *√2 = 5√2
    h = (1.5) b = (1.5) *(5) (
Explanation:
Area of a triangle:Â A = 1/2 * base * height = 1/2 * b * h ;
Given: Â b = 1.5 h ;
      A = 75 units²
Solve for "h" ("height") ; Â h = 1.5 b ;
So, we solve for "b" ; then we plug that value into the equation:Â
 Â
    →  h = 1.5 b ;  to get the height, "h" ;
    →  75 = 1/2 * (b) (1.5 b) ;
     Multiply the ENTIRE equation by "2" ;Â
 to get rid of the fraction and decimals ;Â
    →  2 * { 75 = 1/2 * (b) (1.5 b) } ;
    →  150 =  b * 3b ;
    →  150  =  3 b²  ; Â
Â
    ↔ 3 b² =  150 ;Â
Â
      Now, divide EACH side of the equation by "3" ;
    →  3 b² / 3 = 150 / 3 ;Â
    →   b²  = 50 ;
      Now, take the POSITIVE square root of each side of the equation;Â
to isolate "b" on one side of the equation; and to solve for "b" ;
     →  √(b²)  =  √50
     →    b  =  √50
     →    b  =  √50 = √25 *√2 = 5√2
    →    h = 1.5 * 5 * √2 ;
    →  h = (7.5 √2)  units ;
             Â
           or,  (7.5) * (√2) = 10.6066017177982129 units ;
                       → round to 10.61 units .