Maths question need answer urgently please help much aprpreciated

Question

A radio ham places an aerial mast where it gives the best reception on the roof of his rectangular garage. He then fixes wire supports from the top of the mast to each corner of the roof. The lengths of two opposite supports are seven metres and four metres and the length of one of the others is 1 metre. Find the length of the remaining support.

Answer 1

EDITED ANSWER:
 
Word (story) problems are simply "made up" math examples.  Therefore, you must look for clues that are math figures, operations, equations, etc.
 
This problem mentions "rectangular garage".  It often helps to draw a picture so you can visualize the situation.
 
Now, "where it gives the best reception on the roof" means that, somewhere inside that rectangle, there is an aerial mast.
 
"The lengths of two opposite supports are seven metres and four metres" (please draw that now) gives some distance information.  "Opposite supports" mean wire supports that go from the mast to opposite corners of the rectangle.  Even though your picture may not be to scale, label those two line segments.
 
"the length of one of the others is 1 metre" gives the length of one of the remaining segments, so label it.
 
"Find the length of the remaining support" is the unknown (we often use x for an unknown), so label that segment x.
 
(EDITED)  Now, realize that there is some important information missing:
    1) is the roof flat?    So, assuming a flat roof (it is a garage) and a very short aerial mast [note:  after all the length of one support is 1 metre], we have a rectangle with lines going from the four corners to a point somewhere within the rectangle (not a perfect “X”).
    2) how tall is the aerial mast.   Note that if one support is 1 metre in length, we might ignore this height.
 
So, can a rectangle be formed using points on circles of radius 1, 4, 7, and x from the aerial mast?   [mast must be internal to rectangle]
 
Yes.  [note: maths explanation, not trig]
 
Let the point of "best reception" be along one side of the roof (that is, the rectangle) with distances of 4 and 1 to the corners. Then, let the hypotenuse from the aerial mast to an opposite corner be 7.  The distance from the aerial mast to the other opposite corner is x   (Are you drawing this?).  That gives right triangles with sides:
      4, y, 7          [we won't need to know y]
      1, y, x
 
Now use the Pythagorean Theorem:
    4² + y² = 7²        and   1² + y² = x²
    y² = 7² - 4² 
Let's determine x:
    x² = 1² + y²
    x² = 1 + (72 - 42)
    x² = 1 + 49 - 16
    x² = 34
     x = √34
 
Again note that the problem asked you to find the length of the remaining support; you never have to determine the length of the remaining side of the rectangle.