Trapeze call a quadrangle which bases lie on two parallel straight lines, at the same time two other parties parallel are not. Finding of the basis of an isosceles trapeze is required as at delivery of the theory and the solution of tasks in educational institutions, and in a number of professions (engineering, architectural, design).
Instruction
1. At isosceles (or ravnoboky) the nonparallel parties as well as corners which are formed when crossing the lower basis are equal to a trapeze.
2. The trapeze has two reasons and that to find them, it is necessary to designate a figure at first. Let the isosceles trapeze of ABCD with the bases of AD and BC be given. At the same time all parameters, except the bases are known. AB=CD=a side, height of BH=h and the area is equal to S.
3. For the solution of a task on the basis of a trapeze it will be simplest to work out the system of the equations that through the interconnected sizes to find the necessary bases.
4. Designate BC piece for x, and AD for y that further it was convenient to handle formulas and to understand them. If not to make it at once, it is possible to get confused.
5. Write out all formulas which will be useful at the solution of an objective, using the known data. Formula of the area of an isosceles trapeze: S=((AD+BC)*h)/2. Pythagorean theorem: a*a = h*h + AH*AH .
6. Remember property of an isosceles trapeze: heights leaving trapeze top cut equal pieces on the big basis. From this it follows that two bases can be connected on the formula following from this property: AD=BC+2AH or y=x+2AH
7. Find AH leg, following Pythagorean theorem which you already wrote down. Let it be equal there will be nobody number k. Then the formula following from property of an isosceles trapeze will look so: y=x+2k.
8. Express unknown size through the area of a trapeze. At you it has to turn out: AD=2*S/h-BC or y=2*S/h-x.
9. After that substitute these numerical values in the received system of the equations and solve it. A solution of any system of the equations can be found automatically in the MATHCAD program.