Question

the perimeter of a right angled triangle is 12 cm and its hypotenuse is of length 5 cm. find the others sides and calculate its area by heron's formula​

Answer 1

Answer:

3,4,&5 are Pythagorean triplet and also 3+4+5=12

thus the other two sides are 3cm&4cm

s=12/2=6cm

area=

$\sqrt{s \times (s - a )\times (s - b) \times (s - c)}$

here a= 5 , b= 4 and c=3

$\sqrt{6 \times (6 - 5)(6 - 4)(6 - 3) } \\ \sqrt{6 \times 1 \times 2 \times 3} \\ \sqrt{2 \times 3 \times 1 \times 2 \times 3} \\ 2 \times 3 = 6 {cm}^{2}$