Home > Geometry > Perimeter and Area of Triangle

Two corners of an isosceles triangle are at #(3 ,9 )# and #(2 ,5 )#. If the triangle's area is #4 #, what are the lengths of the triangle's sides?

Answer 1

Sadie Allen

The lengths of the triangle's sides are #2.83#, #2.83# and #4.12#

The length of the base is

#b=sqrt((3-2)^2+(9-5)^2)=sqrt(1^2+4^2)=sqrt17#

Let the height of the triangle be #=h#

The area is

#A=1/2*b*h#

#1/2*sqrt17*h=4#

#h=(4*2)/(sqrt17)=8/sqrt17#

Let the lengths of the second and third sides of the triangle be #=c#

Then,

#c^2=h^2+(b/2)^2#

#c^2=(8/sqrt17)^2+(sqrt17/2)^2#

#c^2=3.76+4.25=8.01#

#c=sqrt(8.01)=2.83#

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

Answer 2

Theodore Abad

The lengths of the triangle's sides are approximately 3.20, 3.20, and 5.64 units.

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.