Question

The base of a triangle is one third as long as its height. if the area of the triangle is 6 square meters, how long is its base

Answer 1

The answer is:  " 2 m" . 
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Explanation: 
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The formula for the area, "A" , of a TRIANGLE is:
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 A = (1/2) * b * h  ;    or, write as:  " A = (b * h) / 2 " ; 
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    in which:  A = area of triangle; 
                     b = length of base; 
                     h = [perpendicular] height .
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 We are given:  "b = 1/3 h  = h/3" ; 
                          "A = 6 m²: "

We are asked to solve for "b"  ; 

So:  "A = ( b * h) / 2 " ; 

→ Re-arrange the equation to isolate "b" on one side of the equation ; 

→   "A = ( b * h) / 2 " ; ;

Multiply EACH SIDE of the equation by "2" ; 
→   2 * A = { ( b * h) / 2 } * 2 " ;

to get:

→   2A = b * h ;

↔  b * h = 2A ;

NOTE:   Calculate "2A" ; as follows:   " 2A = 2* 6 m² = 12 m² " ; 

→  b * h = 12 m² ; 

Note:  "b = h/3 " ; 

So rewrite:

→  "b * h = 12 m² ;  

as:  (h/3) * h = 12 m² ; 

→   $\frac{h}{3}$  *  $\frac{h}{1}$ = 12 m² ; 

→  $\frac{(h*h)}{(3*1)} = \frac{h^2}{3} =$  = 12 ; 

→ Now, we can solve for "h" ;  {and then, solve for "b" }..
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We have:  \frac{h^2}{3} = [/tex]  = 12
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    →  h² = 12 * 3 ; 

    →  h² =  36 ; 

Now, take the positive square root of EACH SIDE of the equation; 
    to isolate "h" on one side of the equation; & to solve for "h" ; 

    →  +√(h²)  =  +√36  ; 

    →  h  =  6 m ;

Now, we can solve for "b" ; 

b = h / 3 = 6 m / 3 = 2 m .

→ b = 2 m . 
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The answer is:  " 2 m" . 
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Let us check our answer:
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A = (b * h) / 2 ; 

  → 6 m²  = ?  (2 m  * 6 m) / 2 ??  ; 

  → 6 m²  = ?  (12 m²) / 2 ??  Yes!
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