Ok, num 2.
Let side AO be
, therefore CD is also =
Using similar triangles,
Simplifying:
Then Solve.
num 3.
a) Wait. Do you know about similar triangles? I'll take this number as an example.
You'll find that angle ABE and ACD are equal. Then, they both have an angle in common, that is angle CAD or BAE. Also you have angle BEA and CDA which are equal because of the parallel lines BE and CD and AED is a straight line. Similar triangles have same corresponding angles.
Then, similar triangles also have the ratio of their corresponding sides equal. Take BE.
and
, etc...
Note that you should have all those conditions for two triangles to be similar. These will help you for the work to be done.
b) & c)
Galactus has already given the method
num 6.
Don't understand what's so difficult. You have the area of the base of your box. What do you think is the length of the width, if you have to cut it from a square cardboard and squares are to be removed?
num 7.
a) How would you obtain the area of the pavement? With a drawing, you must find the total area (i.e. pavement + pool) and subtract the area of the pool. What is the total area, if the pavement has a uniform width of
cm? You have
. You can obtain the area of the pool easily. Just do the subtraction and there it is, you have
b) How can you obtain the area of the pavement in another way?
the area of the pavement being 7/8 of the area of the pool Just do the area of the pavement. Therefore,
and put it in the form asked in the question.
c) Solve for x to have the width of the pavement.
num 8 (hum... you mean a hollow cylindrical magnet?)
How do you find the volume of the magnet? Subtract the volume of the 'cylinder' with x as radius from the 'cylinder' with (x+2) as radius. The expression you obtain is equal to
. Solve of x and you're done!
Hope this helped!