Question

How do you find the height of a triangle?

Answer 1

Answers:  height, "h", of a triangle:     h = 2A /  (b₁ + b₂) .
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Explanation:
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The area of a triangle, "A", is equal to (1/2) * (b₁ + b₂) * h ; 
                                    or:  A = (1/2) * (b₁ + b₂) * h
                                    or: write as:  A =  [(b₁ + b₂) * h] / 2 ;
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                                     in which:  A = area of the triangle; 
                                                       b₁ = length of one of the bases
                                                                 of the triangle ("base 1");
                                                       b₂ = length of the other base
                                                                 of the triangle ("base 2");
                                                       h = height of the triangle;
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To find the height of the triangle, we rearrange the formula to solve for "h" (height); assuming that all the units are the same (e.g. feet, centimeters); if no "units" are given, then the assumption is that the units are all the same.
We can use the term "units" if desired, in such cases; in which the area, "A" is measured in "square units"; or "units²",
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So, given our formula for the "Area, "A"; of a triangle:
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 A =  [(b₁ + b₂) * h] / 2 ; we solve for "h" in terms of the other values; by isolating "h" (height) on one side of the equation.
     If we knew the other values; we plug in the those other values.
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  Given:   A =  [(b₁ + b₂) * h] / 2 ;

Multiply EACH side of the equation by "2" ;
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            2*A = {  [(b₁ + b₂) * h] / 2 } * 2 ;
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to get:
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           2A = (b₁ + b₂) * h ;
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           Now, divide EACH side of the equation by:  "(b₁ + b₂)" ;  to isolate "h"
on one side of the equation; and solve for "h" (height) in terms of the other values;
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            2A /  (b₁ + b₂) = [ (b₁ + b₂) * h ] / (b₁ + b₂);
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to get:
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           2A /  (b₁ + b₂)  =  h ;  ↔  h = 2A /  (b₁ + b₂)  .
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