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 ;
→ [tex] \frac{h}{3} [/tex] * [tex] \frac{h}{1} [/tex] = 12 m² ;
→ [tex] \frac{(h*h)}{(3*1)} = \frac{h^2}{3} = [/tex] = 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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