Arectangle that is 8 centimeters long has an area of 100 square centimeters. a similar rectangle has an area of 16 square centimeters. what is the width of the smaller rectangle

The width of the smaller rectangle is 5 centimeters

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x ----> the area of the smaller rectangle

y ----> the area of the larger rectangle

we have

substitute

square root both sides

step 2

Find the width of the larger rectangle

we know that the area is equal to

we have

substitute

step 3

Find the width of the smaller rectangle

To find out the width of the smaller rectangle, multiply the width of the larger rectangle by the scale factor

so

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".