Can You Find The Base And Height For A Triangle You Know The Area Is 22 Square Units?

2 Answers

Simon Templar Profile
Simon Templar answered
The area of a triangle is found by multiplying the base and height and dividing by two.

You have the area - but without knowing either the base or the height, you can't directly find the other.

For instance, if your triangle had a base of 2 units, then the height would be 22 units.  A triangle with those proportions would have an area of 22 square units.

Similarly, if your triangle had a base of 4 units, then the height would be 11 units.  Such a triangle would also have an area of 22 square units.

In fact, if you can find two numbers that, when multiplied give you 44, they can comprise the base and height of a triangle whose area is 22 square units.

So the literal answer is "yes"; but the exact mathematical value is no - not without more information.
Jack TheJaxter Profile
Jack TheJaxter answered
Simon's right, but the answer is more simple:  Any triangle with a base and height that result in the given area is a valid answer.  In fact, there are an unlimited number of them.  They're height and base are related like this: Let's say Area is A, Height is H and Base is B.  So, A = 1/2 x H x B.  If I divide the equation by B, I get A / B = 1/2 x H  if I divide it by 1/2 (the same as multiplying by 2), I get  2 x A / B = H    or H = 2 x A / B  now imagine a graph where you put Base on the x-axis (the horizontal one), and Height on the y-axis (the vertical one).  For any positive value of B (say, 4), there's only one corresponding value of H (in this case, 11).  You can find the H for each B using the equation  H = 2 x A / B where A = 22, in your example. So, the equation becomes H = 44 / B    So, when B = 1, then H = 44.  When B = 2, H = 22, etc.if you were to put a dot where the B's and H's match for each B you tried, you'd find yourself drawing a curve.  That curve represents the equation H = 44 / B.  Any point on that curve gives a valid pair of B and H that answers your question.  B can't be zero; it must always be positive; that's true for H also.  As either one gets to be outrageously large, the other shrinks to become incredibly small, but you can get as wide or as high as you like.

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