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

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Answer 1 · 2016-02-28T11:04:15

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

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

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

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

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

Two corners of an isosceles triangle are at (1 ,2 )(1,2)(1 ,2 ) and (1 ,7 )(1,7)(1 ,7 ). If the triangle's area is 64 6464 , what are the lengths of the triangle's sides?