Can You answer the question in parenthesis "Li Mei builds a quadrilateral with sides that are each 5 inches long.To help stabilize the quadrilateral, she wants to insert a 10 inch diagonal. Will that work? Explain."
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2 Answers

"quadralateral"=a shape with 4 sides, such as a REKTANGEL

???? maebee yu nael tugether 4 bords tu make the shape ???

??? then yu wana put a diagonal bord kross kanty-korner ???

if "eech side be 5 inch", maebee thang be a SQUARE????????

Leng av the diagonal=sqrt(2)*leng=sqrt(2)*5 inch

=1.41421 35623 73095 04880 16887 24209*5

=7.07106781186548 inch

Yer 10 inch be 2 long, but mite werk is yu nael bords...1 end stik out
by

The quadrilateral she plans to construct must be a square or a rhombus, because each side is 5 in. long.

Label each vertex of the quad. A,B,C and D counterclockwise from the bottom left, so side CD parallel to side AB, side BC to side AD.   The diagonal AC is a bracing to stabilize the shape of the quad.

Notice the fact that, in a triangle, the sum of the lengths of any 2 sides must be greater than the third side.

But, from the conditions given, AB=BC=5 in. long and AC=10 in. long, so AB+BC=AC.   This doesn't agree with the fact mentioned above: AB+BC>AC.

If AC=10 in. long, each vertex A,B,C and D lies on the same straight segment AC, collinear.   There certainly are 4 sides, but not 4 inner angles.   There never be a quad.

Therefore, her plan won't work well, unless the bracing is cut shorter than it is.   

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