Alice drew a rectangle with a perimeter of 30 cm and an area of 56 cm2. Which dimensions match Alice's rectangle?

The dimensions that match Alice's rectangle are 7 cm and 8 cm.

Step-by-step explanation:

The perimeter of the rectangle is given by:

   (1)                              

Where a and b are the sides of the rectangle

Also, the area of the rectangle is:

  (2)

By solving equation (1) for a, we have:

     (3)                      

Now, by entering equation (3) into (2) we can find one side of the rectangle:

Solving the above quadratic equation we have:

b₁ = 7 cm  and b₂ = 8 cm                      

Now, the other side of the rectangle can be calculated with equation (3):

or    

Taking the first solution (b₁) or the second (b₂), we find that the dimensions that match Alice's rectangle are 7 cm and 8 cm.          

Therefore, the dimensions that match Alice's rectangle are 7 cm and 8 cm.

I hope it helps you!                            

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32