CBSE Class 10 Answered
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.