# Two corners of an isosceles triangle are at #(9 ,2 )# and #(1 ,7 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

The length of three sides of triangle are

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

The sides are

The area of the triangle is

The equation of the altitude is

The circle with equation

The intersection of this circle with the altitude will give the third corner.

We solve this quadratic equation

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

Use the formula for the area of a triangle: Area = 0.5 * base * height. Since the triangle is isosceles, the height can be found by drawing a perpendicular line from the vertex opposite the base to the midpoint of the base. Then, use the distance formula to find the length of the base, which is the distance between the two given points. Finally, use the Pythagorean theorem to find the lengths of the remaining sides, which are congruent.

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

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.

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.

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.

- What is the area of a hexagon where all sides are 8 cm?
- An isosceles triangle has sides that are #sqrt125#, #sqrt125#, and 10 units. What is its area?
- What is the largest rectangle that can be inscribed in an equilateral triangle with sides of 12?
- The base of a triangular pyramid is a triangle with corners at #(5 ,8 )#, #(4 ,3 )#, and #(9 ,4 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?
- A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #7 # and #5 # and the pyramid's height is #4 #. If one of the base's corners has an angle of #pi/3#, what is the pyramid's surface area?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7