Answers: height, "h", of a triangle: <span> h = 2A / (b₁ + b₂) . ___________________________________________________ </span> Explanation: __________________________________________________ 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 ; ___________________________________________ 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; ____________________________________________________ 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", _________________________________ So, given our formula for the "Area, "A"; of a triangle: _________________________________________________ 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. ______________________________________________ Given: A = [(b₁ + b₂) * h] / 2 ;
Multiply EACH side of the equation by "2" ; _________________________________________ 2*A = { [(b₁ + b₂) * h] / 2 } * 2 ; _________________________________________ to get: _________________________________________ 2A = (b₁ + b₂) * h ; _____________________________________________________ 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; _____________________________________ 2A / (b₁ + b₂) = [ (b₁ + b₂) * h ] / (b₁ + b₂); ______________________________________ to get: _______________________________________________ 2A / (b₁ + b₂) = h ; ↔<span> h = 2A / (b₁ + b₂) . __________________________________________________</span>
I'm not sure how to write the rule, but every time you add one more to the sum of the last two. First, you add 1, then 2, then 3. 1+1=2 2+2=4 4+3=7 7+4=11 and so on. I hope this helps!
