Question

The base of the triangle is one and a half times it's height. what is height if area is 75

Answer 1

H=15cm
b=10cm 
i think, i asked my mom thats a teacher and she said it was correct.

Answer 2

Answer:  The height is: 10.61 units. 
                       {or, write as:  "(7.5 √2)  units"}. 
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Explanation:
_____________________________________________________
Area of a triangle:  A = 1/2 * base * height = 1/2 * b * h ;

Given:  b = 1.5 * h ;
           A = 75 units²
______________________________
Solve for "h" ("height") ;  h = 1.5 b ;
_________________________________
So, we solve for "b" ; then we plug that value into the equation: 
  
        →   h = 1.5 b ;  to get the height, "h" ;
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        →   75 = 1/2 * (b) (1.5 b) ;
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         Multiply the ENTIRE equation by "2" ;
  to get rid of the fraction and decimals ; 
______________________________________________________
       →   2 * { 75 = 1/2 * (b) (1.5 b) } ;
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       →  150  =  b * 3b ;
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       →  150  =  3 b²  ;  
 
       ↔ 3 b²  =  150 ; 
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            Now, divide EACH side of the equation by "3" ;
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       →  3 b² / 3 = 150 / 3 ; 
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       →     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
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        →      b  =  √50
_________________________________________________
        →     √50 = √25 *√2 = 5√2
_________________________________________________
        h = (1.5) b = (1.5) *(5) (
_____________________________________________________
Explanation:
_____________________________________________________
Area of a triangle:  A = 1/2 * base * height = 1/2 * b * h ;

Given:  b = 1.5 h ;
           A = 75 units²
______________________________
Solve for "h" ("height") ;  h = 1.5 b ;
_________________________________
So, we solve for "b" ; then we plug that value into the equation: 
  
        →   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 ; 
______________________________________________________
       →   2 * { 75 = 1/2 * (b) (1.5 b) } ;
______________________________________________________
       →  150  =  b * 3b ;
______________________________________________________
       →  150  =  3 b²  ;  
 
       ↔ 3 b²  =  150 ; 
______________________________________________________
 
            Now, divide EACH side of the equation by "3" ;
_________________________________________________
       →  3 b² / 3 = 150 / 3 ; 
_________________________________________________
       →     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
_________________________________________________
        →      b  =  √50 = √25 *√2 = 5√2
_________________________________________________
        →      h = 1.5 * 5 * √2 ;
_________________________________________________
       →    h = (7.5 √2)  units ;
                           
                      or,  (7.5) * (√2) = 10.6066017177982129 units ;
_______________________________________________________
                                            → round to 10.61 units .
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