Mathematics

Problem

\triangle XYZ

\angle Y = 90^\circ

. The perpendicular from

Y

to the hypotenuse

XZ

meets

XZ

T

. The hypotenuse is divided such that

XT = x\,\text{cm}

and

TZ = (x + 3)\,\text{cm}

. If

XY = 9\,\text{cm}

, answer the following: a. (i) Express the length of

XZ

in terms of

x

. b. (ii) Form an equation in

x

and solve for the possible value(s) of

x

. c. (iii) Find the length of the altitude

YT

. d. (iv) Determine the exact length of the hypotenuse

XZ