A piece of wire 400cm long is bent to form the perimeter of a right langted triangle whose hypotenuse is170mm find the length of the shortor side.

Answer 1

Mark the shorter pages with a and b and mark the hypotenuse with c.

The perimeter is:

P = a + b + c = 400 cm

a + b + 170 = 400

Subtract 170 from both sides

a + b = 230

The length of the hypotenuse is:

c = √ (a² + b²)

170 = √ (a² + b²)

Square both sides

28900 = a² + b²

Now you need to solve the system:

a + b = 230

a² + b² = 28900

From the first equation:

a = 230 - b

Put this in the second equation.

( 230 - b )² + b² = 28900

When you compose the equation it will be:

2 b² - 460 b + 24000 = 0

Divide both sides by 2

b² - 230 b + 12000 = 0

The solutions are:

b = 80

and

b = 150

when b = 80 cm

a = 230 - b = 230 - 80 = 150 cm

when b = 150 cm

a = 230 - b = 230 - 150 = 80 cm

So the shorter sides are 80 cm and 150 cm