# 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 #18 # and the triangle has an area of #72 #. What are the lengths of sides A and B?

Given :

As Area

where

Here,

By Pythagorean theorem, we know that

Hence,

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Using the formula for the area of a triangle, ( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} ), and knowing that the triangle is isosceles, where sides ( A ) and ( B ) are equal, we can set up the equation:

[ 72 = \frac{1}{2} \times A \times h ]

Given that the height (( h )) can be calculated using the Pythagorean theorem with ( C = 18 ) and ( A = B ):

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

Once you have found ( h ), you can solve for ( A ) and ( B ) using the area equation and the fact that ( A = B ).

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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.

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