Question

the perimeter of a right triangle is 144 cm and its hypotenuse measures 65 cm find the length of the Other sides and find its area. verify the results using heron's formula.

Answer 1

Length of side 1 is 16cm
Length of side 2 is 63 cm
Length of side 3 is 65 cm

Using hero's formula, area of triangle = squareroot of S(S-a)(S-b)(S-c)
[S=half perimeter of triangle]
=squareroot of72(72-16)(72-63)(72-65)
=squareroot of 72×56×9×7
=squareroot of 254016
=504
Therefore, area triangle = 504 sq.cm