# An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #8 # and the triangle has an area of #32 #. What are the lengths of sides A and B?

Area of a triangle

Given that

Hence,

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

Using the formula for the area of a triangle, ( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} ), where in the case of an isosceles triangle, the base is one of the equal sides (let's say ( A )) and the height is the perpendicular distance from the base to the opposite vertex (let's say ( h )), we can set up the equation:

( 32 = \frac{1}{2} \times A \times h )

Given that side ( C ) is 8 units long, it can be seen as the base of two right triangles, each formed by ( A ), ( B ), and half of ( C ). Using the Pythagorean theorem, the height ( h ) can be expressed as:

( h = \sqrt{C^2 - \left(\frac{C}{2}\right)^2} )

Substitute the given values:

( h = \sqrt{8^2 - \left(\frac{8}{2}\right)^2} = \sqrt{64 - 16} = \sqrt{48} = 4\sqrt{3} )

Now, substitute the values of ( h ) and the given area into the area formula:

( 32 = \frac{1}{2} \times A \times 4\sqrt{3} )

Solve for ( A ):

( 32 = 2A\sqrt{3} )

( A\sqrt{3} = 16 )

( A = \frac{16}{\sqrt{3}} = \frac{16\sqrt{3}}{3} )

Since sides ( A ) and ( B ) are equal in length:

( A = B = \frac{16\sqrt{3}}{3} )

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.

- In a 30-60-90 triangle, the shorter leg has length of #8sqrt3# m. What is the length of the other leg (L) and the hypotenuse?
- What is a hypotenuse?
- The hypotenuse of a right triangle is 25 cm, and the shorter leg is 15 cm. What is the length of the other leg?
- If A is an acute angle and sin A = .8406, what is angle A round to the nearest tenth of a degree?
- How do you use the pythagorean theorem to solve a=x-5 b=x 2 c=13?

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