Question

find the area of a right angle with one of the sides and hypotenuse as 3 cm and 5 cm by heron's formula​

Answer 1

a+b+5=12

a+b=7⇒a=7−b...(1)

a

2

+b

2

=5

2

a

2

+b

2

=25...(2)

From (1) and (2)

(7−b)

2

+b

2

=25

49+b

2

−14b+b

2

=25

2b

2

−14b+24=0

b

2

−7b+12=0

(b−4)(b−3)=0

⇒b=4,3

a=7−b⇒a=3,4

Area=

2

1

×4×3=6sq. units