Question 767178
Q:
The legs of a right triangle are 3 and 4 units long. Find the lengths, to the nearest tenth, of the segments into which the bisector of the right angle divides the hypotenuse
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A:
{{{drawing(300,300,-3,5,-3,5,grid(1),blue(line(0,4,3,0)),line(0,0,12/7,12/7),blue(line(0,0,3,0)),blue(line(0,0,0,4)),locate(1,1,"h"),locate(1,3,"m"),locate(2.5,1,"n"))}}}
The equation of the bisector is y = x.
The equation of the hypotenuse is {{{y = (-4/3)x + 4}}}.
Solving for the point of intersection of the bisector and hypotenuse:
x = {{{(-4/3)x + 4}}}
{{{(7/3)x}}} = 4
x = {{{12/7}}} = y
Therefore the point of intersection is ({{{12/7}}},{{{12/7}}}).
Using distance formula:
m = {{{sqrt((0 - 12/7)^2 + (4-12/7)^2 )}}} ≈ 2.9
n = {{{sqrt((12/7 - 3 )^2 + (12/7 - 0)^2)}}} ≈ 2.1
ANSWERS: {{{highlight(2.9)}}}, {{{highlight(2.1)}}}