Question

If the length of the base of a thin right triangular sheet is decreased by 1 cm and perpendicular side is increased by 1 cm, the area of the triangular sheet remains unchanged. If the base and the perpendicular side each is increased by 1 cm, the resulting area increased by 4 cm sq. Find the length of the base and the perpendicular side of the right triangle.

Answer 1

A TO Q.
in 1st case.
area of the triangle = 1/2.b.h
in 2nd case.
area of the triangle = 1/2.(b-1).(h+1)
but we have area in each case is equal.
so,1/2.b.h = 1/2.(b-1).(h+1)
b.h = b.h + b - h -1
b-h = 1.
b = 1+h...........(1)
NOW,
area of the triangle is 1/2.(b+1).(h+1)
but it is increased by 4 cm^2.
so,1/2.(b+1).(h+1) =( 1/2 .b.h )+ 4
1/2(b.h+b+h+1) = (1/2.b.h) + 4
by putting the value of b from equation 1 ,we get
1/2{(1+h)h+1+h+h+1} = 1/2.(1+h)h+4
1/2(h^2+3h+2) = 1/2(h^2+h)+4
1/2(h^2)+1/2(3h)+1 = 1/2(h^2)+1/2(h)+4
(3h/2)+1 = (h/2)+4
3h/2 - h/2 = 3
2h/2 = 3
h = 3.