please answer this question

Asked by mac12303190 | 1st Mar, 2010, 11:44: PM

Expert Answer:

basic theory behind this question

suppose a  right triangle ABC has sides a,b and hypo c

a=BC

b=AC

c=AB

then the area of this triangle is=[1/2][ab]

let O be the incenter. drop perpendiculars from O to the sides BC,CA and AB

Join O to A,B,C

so area of triangle ABC  can be written as the sum of areas of triangles

AOB,BOC,COA

so

ab/2=rb/2+rc/2+ra/2

i.e.

ab/2=[r/2][a+b+c]

i.r.

r=ab/[a+b+c]

 

now for the given question

let the two sides be a,b. hypo=13 given

 area=30

so 1/2[ab]=30

i.e. ab=60

i.e. b=60/a

now put these values in the formula for r and you can get the answer.

depending on the marks allotted to the question you can increase the length of the solution.

 e.g. if it comes for say 6 marks, it's advisable to show the entire calculations using the theory shown above.

in any case draw the diagram as mentioned in the solution.

Answered by  | 2nd Mar, 2010, 10:52: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.