What is the perimeter of a right angle triangle whose hypotenuse is 6.5 cm and has an area of 10.14 square cm showing work done?

Answer 1

Let its sides be squared x and squared y:-

Using Pythagoras: x+y = 42.25 => y = 42.25-x

Area: xy = (10.14*2) squared => x(42.25-x) = 411.2784

S: 42.25x -x^2 -411.2784 = 0

Solving the quadratic equation: x = 15.21 or x = 27.04

Square root of 15.21 = 3.9 and square root of 27.04 = 5.2

When x = 3.9 then y = 5.2

Perimeter of the triangle: 3.9+5.2+6.5 = 15.6 cm

Answer 2

Suppose the 2 legs of the triangle are x and ythen, by Pythagoras, x^2 + y^2 = 6.5^2 = 42.25

Also, Area = x*y/2 so that y = 2*Area/x = 20.28/x

Therefore, x^2 + (20.28/x)^2 = 42.24

Multiply by x^2: x^4 + 20.28^2 = 42.24*x^2

tis is a quadratic in x^2 and its roots are x^2 = 15.21 or x^2 = 27.04

Therefore, x = 3.9 or x = 5.2

then, solving for y gives (x, y) = (3.9, 5.2) or (5.2, 3.9)

and so the perimeter is 3.9 + 5.2 + 6.5 = 15.6 cm.