The hypotenuse of a right triangle is 8 cm longer than the longer leg. The shorter leg is 17 cm shorter than the longer leg. Find the length of the longer leg of the triangle.

  45 cm

Step-by-step explanation:

Let x represent the length of the longer leg. Then the hypotenuse is x+8 and the shorter leg is x-17. The Pythagorean theorem gives the relation between these values as ...

  (x +8)^2 = x^2 +(x -17)^2

  x^2 +16x +64 = 2x^2 -34x +289 . . . . eliminate parentheses

  0 = x^2 -50x +225 . . . . . put in standard form

  0 = (x -45)(x -5) . . . . . . . . factor

Solutions to this equation are x=5 and x=45. The value of x must be greater than 17, so the useful solution is x=45.

The length of the longer leg of the triangle is 45 cm.

45

Step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

step-by-step explanation: