The hypotenuse of a right triangle is 9 feet more than the shorter leg and the longer leg is 15 feet. How do you find the length of the hypotenuse and shorter leg?

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Answer 1 · 2018-04-20T11:23:57

#color(blue)("hypotenuse"=17)#

#color(blue)("short leg" = 8)#

Let #bbx# be the length of the hypotenuse.

The shorter leg is 9 feet less than the hypotenuse, so the length of the shorter leg is:

#x-9#

The longer leg is 15 feet.

By Pythagoras' theorem the square on the hypotenuse is equal to the sum of the squares of the other two sides:

#x^2=15^2+(x-9)^2#

So we need to solve this equation for #x#:

#x^2=15^2+(x-9)^2#

Expand the bracket:

#x^2=15^2+x^2-18x+81#

Simplify:

#306-18x=0#

#x=306/18=17#

The hypotenuse is #17# feet long.

The shorter leg is:

#x-9#

#17-9=8# feet long.