word problem

Question

a toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 2 cm more than the shorter leg and the hypotenuse 4 cm more than the shorter leg. how long should the sides of the triangle be.

 

might have to separate answers

Answer 1

Macy,

 

Let         x = length of shortest leg of right triangle (in cm)

     (x + 2) = length of longer leg (in cm)

     (x + 4) = length of hypotenuse (in cm)

 

Now for a right triangle use the c² = a² + b² formula that relates the 3 sides of the triangle.

Then

     (x + 4)² = x² + (x + 2)² .  Expand this

     (x² + 8x + 16)  =  x²  +  (x² + 4x + 4) ,   then combine terms on the right side

     0  =  x² - 4x - 12 ,  We can use the quadratic formula to solve this, but it's simpler in this case to factor it.

     0  =  (x - 6) ( x + 2) ,  for the product of the 2 factors to be zero, one or both have to be zero

 

So first try (x + 2) = 0  implies x = -2 cm  , but triangle side can't be negative, so discard this solutionn

    next try (x - 6)  = 0  implies x = 6 cm.

 

So your right triangle has sides : 6 cm , 8 cm and 10 cm for the hypotenuse.

 

Check:  (10)² =? (6)² + (8)² ,

            100   =   36   +   64   = 100  so it checks as the correct unique solution.

Answer 2

Hello Macy,

 

The triangle you need is a 6,8,10 right triangle.