Find the value of x.

9514 1404 393

  (b)  48

Step-by-step explanation:

In this geometry, the altitude (x) is the root of the product of the segments of the hypotenuse.

  x = √(36·64) = √36×√64 = 6×8

  x = 48

All of the triangles are similar, so the ratios of corresponding sides are the same.

  short side/long side =  x/64 = 36/x

  x^2 = (64)(36) . . . .  as above

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:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.