SOLUTION: 1.please help me to solve this problem abcd is quadrilateral prove that (ab+bc+cd+da)>(av+bd) 2.find the length of hypotenuse of right triangle,the other two sides are 9 cm,12 cm

Question 947539: 1.please help me to solve this problem abcd is quadrilateral prove that (ab+bc+cd+da)>(av+bd)
2.find the length of hypotenuse of right triangle,the other two sides are
9 cm,12 cm

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
1. Points A, B, C, and D are the vertices of the quadrilateral
(I write them as capital letters, because points are usually named that way),
but what point is V? Or did you mean B?
If ABCD is quadrilateral,
BD is a diagonal, and of course
BD < BC + CD
That is because a straight line is the shorter distance between two points,
or because the length of a side of any triangle (such as side BD of triangle BCD)
is less than the sum of the lengths of the other two sides (sides BC and CD).
Those are two ways of saying the same thing.
So, since BD < BC + CD,
then, BD < BC + CD ---> AB + BD < AB + BC + CD < AB + BC + CD +DA

2. What your teacher expects is that you use a calculator and the Pythagorean theorem,
that says that for a right triangle,
the square of the length of the hypotenuse is
the sum of the squares of the lengths of the other two sides (called legs).
In your case, with the lengths in cm,

Now (unless you remember squares of small numbers as I do),
you use a calculator to find that square root, and get
,
so the length of the hypotenuse is .

However, if you do not have to show your work,
and especially if you need to solve the problem quickly for a timed test,
there is a faster way to the answer:
A very popular Pythagorean triple is (3,4,5),
meaning that a right triangle with legs measuring 3, and 4,
has a hypotenuse measuring 5 (measured in whatever units you choose).
That triangle can be scaled up, by multiplying all measurements by the same number.
Multiplying times 2, we get the triple (6,8,10);
multiplying times 3, we get

.
So, I do not need to to do much calculation to know that in a right triangle,
if the lengths of the legs are cm, and cm ,
the length of hypotenuse is .
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