Home > Geometry > Perimeter and Area of Triangle

Two corners of an isosceles triangle are at #(1 ,5 )# and #(3 ,7 )#. If the triangle's area is #4 #, what are the lengths of the triangle's sides?

Answer 1

The lengths of the sides are: #4sqrt2#, #sqrt10#, and #sqrt10#.

Let the given line segment be called #X#. After using the distance formula #a^2+b^2=c^2#, we get #X=4sqrt2#.

Area of a triangle #=1/2bh# We are given the area is 4 square units, and the base is side length X.

#4=1/2(4sqrt2)(h)# #4=2sqrt2h# #h=2/sqrt2# Now we have the base and the height and the area. we can divide the isosceles triangle into 2 right triangles to find the remaining side lengths, which are equal to each other. Let the remaining side length = #L#. Using the distance formula: #(2/sqrt2)^2+(2sqrt2)^2=L^2# #L=sqrt10#

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

Answer 2

Mason Adams

The lengths of the sides of the isosceles triangle are ( \sqrt{5} ) and ( 2\sqrt{2} ) 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.