MathDB

Source: 2017 Canadian Open Math Challenge, Problem C3 —-- Let

XYZ

be an acute-angled triangle. Let

s

be the side-length of the square which has two adjacent vertices on side

YZ

, one vertex on side

XY

and one vertex on side

XZ

. Let

h

be the distance from

X

to the side

YZ

and let

b

be the distance from

Y

Z

.
[asy] pair S, D; D = 1.27; S = 2.55; draw((2, 4)--(0, 0)--(7, 0)--cycle); draw((1.27,0)--(1.27+2.55,0)--(1.27+2.55,2.55)--(1.27,2.55)--cycle); label("

X

",(2,4),N); label("

Y

",(0,0),W); label("

Z

",(7,0),E); [/asy]
(a) If the vertices have coordinates

X = (2, 4)

Y = (0, 0)

and

Z = (4, 0)

, find

b

h

and

s

. (b) Given the height

h = 3

and

s = 2

, find the base

b

. (c) If the area of the square is

2017

, determine the minimum area of triangle

XYZ

Problem Statement