Two corners of an isosceles triangle are at #(1 ,2 )# and #(1 ,7 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

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Answer 1 · 2016-02-28T11:04:15

#"The sides length is "25.722# to 3 decimal places
#"The base length is "5 #

Notice the way I have shown my working. Maths is partly about communication!

Tony B

Let the #Delta #ABC represent the one in the question

Let the length of sides AC and BC be #s#
Let the vertical height be #h#
Let the area be #a = 64" units"^2#

Let #A ->(x,y)->(1,2)#
Let #B->(x,y)->(1,7)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To determine the length AB")#

#color(green)(AB" " = " "y_2-y_1 " "=" " 7-2" "=" 5)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To determine the height "h)#

Area = #(AB)/2 xx h#

#a=64 = 5/2xxh#

#color(green)(h=(2xx64)/5 = 25.6)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To determine side length "s)#

Using Pythagoras

#s^2=h^2+((AB)/2)^2#

#s=sqrt((25.6)^2+(5/2)^2)#

#color(green)(s= 25.722" to 3 decimal places")#