One leg of a right triangle is 96 inches. How do you find the hypotenuse and the other leg if the length of the hypotenuse exceeds 2.5 times the other leg by 4 inches?

1 Answer
Jan 15, 2016

Answer:

Use Pythagoras to establish #x=40# and #h =104#

Explanation:

Let #x# be the other leg
then the hypotenuse # h=5/2x +4#
And we are told the the first leg #y= 96#

We can use Pythagoras' equation #x^2 +y^2 = h^2#
#x^2 +96^2 = (5/2x+4)^2#
#x^2 + 9216 = 25x^2/4 +20x +16#

Reordering gives us
#x^2 - 25x^2/4 -20x +9200 = 0#

Multiply throughout by #-4 #
#21x^2 +80x -36800 = 0#

Using the quadratic formula #x= (-b+-sqrt(b^2 - 4ac))/(2a)#

#x =( -(80) +- sqrt(6400 + 3091200))/(-42)#
#x = (-80 +-1760)/42#

so #x = 40# or #x = -1840/42#

We can ignore the negative answer as we re dealing with a real triangle, so the other leg #=40#

The hypotenuse #h = 5*40/2 +4 =104#