Mathhemathh

Number 5 asks for the greatest solution, and it's not 100.

x = girl's age

2x = mom's age

2x + 5 = father's age

\(x + 2x+2x+5=100\)

\(5x+5=100\)

\(5x=95\)

\(x = 19\)

The girl's age is 19, the mother's age is 19*2 or 38, and the father's age is 38+5 or 43.

CHECK: 19 + 38 + 43 = 100?

               100 = 100

That is equal to 2.557654 * 10^60, or approx. 2557654000000000000000000000000000000000000000000000000000000

I did stuff, and here's what I got:

First of all, apparently you can't even make a trapezoid with your measurements; only two sides are congruent, and none can be parallel. Secondly, you can draw a figure like this using the 3-4-5 right triangle:

     C

4  /

   /  D

         |\            

        4 |  \   5       

         |__\        

A   3  B

Pretend there is a line connecting B and C that measures 6

Now we know the length of DB, 5. This means that DB cannot be the longest diagonal. The longest diagonal has to be longer than any of the sides. So we have to find a number that is greater than 6 BUT less than 8, because of the triangle inequality theorem (thanks) which states that the sum of any 2 sides must be greater than the 3rd side. The sum of the sides of the triangle formed is 4+4, or 8, which means it can't be greater than 8. And since its length is an integer, AC has to be 7. That's all I could think of.

Multiply the length of the base by the height of the triangle, then divide the result by 2.

For example: 

  /  \     h = 4

/___\   

   3

b = 3

h = 4

The area of this triangle is (3*4)/2, or 6.

Many people have asked the question "why". Why do we die? Why is 1 equal to 1? Some questions have a defined answer. Some, scholars have obsessed over for centuries. Questions such as "why" can become vey significant to the lives of the people. Questions like "why do we pay taxes" or "why can't I find a job" are commonly asked, even if answers to these questions already exist. The point is, many people don't know that a simple "why?" can affect us in exponential ways. But for you, I give the simplest answer, one that many people have used and/or despised for years. I give you...

because.

Uh, do you mean trapezoid? Because given your measurements, the figure can't be a parallelogram. Either only AB and CD or BC and DA can be parallel.

My best illustration:

      T___ O

     /  \     /

   /___\ /

  I       P

TI = 5, PI = 7, PO = 11.

Since they are both isosceles triangles (2 sides are equal), and TI is not equal to PI, then TP has to be equal to TI or PI, meaning TP = 5, 7. Their sum is 12.

Now we know that TP = 5 or 7, which means TP is not equal to PO. Because of this, TO has to be equal to either TP or PO, meaning TO = 5, 7, 11 since TP is either 5 or 7. Their sum is 23.

2A+2B?