Home > Geometry > Perimeter and Area of Triangle

Two corners of an isosceles triangle are at #(1 ,3 )# and #(1 ,4 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

Answer 1

Lengths of sides: #{1,128.0,128.0}#

The vertices at #(1,3)# and #(1,4)# are #1# unit apart.
So one side of the triangle has a length of #1#.

Note that the equal length sides of the isosceles triangle can not be both equal to #1# since such a triangle could not have an area of #64# sq. units.

If we use the side with length #1# as the base then the height of the triangle relative to this base must be #128#
(Since #A=1/2 * b * h# with the given values: #64=1/2 * 1 * hrarr h=128#)

Bisecting the base to form two right triangles and applying the Pythagorean Theorem, the lengths of the unknown sides must be
#sqrt(128^2+(1/2)^2)=sqrt(16385)~~128.0009766#
(Notice that the height to base ratio is so great, there is no significant difference between the height and the length of the other side).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Aurora Ayala

The lengths of the sides of the isosceles triangle are 16 and 8.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.