I have a question about triangles!?

Question

ok im doind my math right now and one of the questions is which triangle has a bigger area. The dimenstions of one called triengle X are 300, 400, and 500. The demenstions of the other one called triangle Y are 300, 400, and 700. Triangle X has the bigger area but smaller sides why is that?

Answer 1

The area of a triangle is 1/2 times length, times height.

The longer side (700) makes the angle of the triangle very obtuse, and that reduces it's height.  A smaller height, reduces the area, if the other two sides stay equal, as in the example.

If you put two triangles together, same size, they form a quadralateral figure, or parrallogram, a four sided figure.  Drawing a line through the two opposite sides makes the two original triangles.  

The formula for figuring area of a quadralatera(with parallel opposite sides)  is length times height, that's why triangles are one half every time.

When there is one side much longer, the quadralateral gets "squeezed", the two opposite sides come closer (height being reduced).

Hard to describe this in words, a picture will make this obvious.

No mystery, only geometry explains your question.

Answer 2

If you draw them out as I did, you can see why.

Answer 3

Kind of hard to explain, but I will try.

Notice that triangle x's side are similar, more like an equilateral, whereas triangle y's has two similar sides and one long one that makes the triangle stretch and get thinner, thereby giving it less area than the equilateral because it is thinner. Make sense?

If it doesn't, draw pictures of the two triangles but with inches. So triangle x would be 3 by 4 by five inches. Then compare them.

Then if that STILL doesn't make sense, think of it in terms of squares. A 5 by 5 square has more area than an 8 by 2 square, so even though the sides of the second square are bigger it is ultimately a smaller square.

Now if that STILL doesn't make sense then...I cannot help.