In the figure, side ab is given by the expression (5x + 5)/(x + 3), and side bc is (3x + 9)/(2x - 4).
the simplified expression for the area of rectangle abcd is and the restriction on x is

The simplified expression for the area of rectangle ABCD is , and the restriction on x is x≠2 .

Step-by-step explanation:

Side AB = Width of rectangle = (5x + 5)/(x + 3)

Side BC = Length of rectangle =  (3x + 9)/(2x - 4)

Area of Rectangle = Length * Width

Putting values:

Solving,

The restriction on x is that x ≠ 2, because if x =2 then denominator will be zero.

So, the answer is:

The simplified expression for the area of rectangle ABCD is , and the restriction on x is x≠2 .

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc