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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