Question

Tristan is working on dilating rectangles. Rectangle ABCD is dilated by a factor of 3. The resulting rectangle WXYZ has an area of 72 cm². Tristan found that the area of rectangle ABCD must be 8 cm². Is he correct? No, because he needs to divide the area of rectangle WXYZ by 3. No, because he needs to multiply the area of rectangle WXYZ by 3. Yes, because he needs to find the possible dimensions for rectangle WXYZ and then divide each dimension by 3. Yes, because he needs to find the possible dimensions for rectangle WXYZ and then multiply each dimension by 3.

Answer 1

Answer:

Tristan is correct, because he needs to find the possible dimensions for rectangle WXYZ and then divide each dimension by 3.

Step-by-step explanation:

The rectangle ABCD is dilated by a factor of 3 to get the rectangle WXYZ whose area is found to be 72 cm².

Let the dimensions of the dilated rectangle WXYZ are a cm by b cm.

So, ab = 72 ........... (1)

Now, the dimensions of the original rectangle are 3 times lesser than the dimensions of rectangle WXYZ.

So, the area of rectangle ABCD will be $(\frac{a}{3} \times \frac{b}{3}) = \frac{ab}{9} = \frac{72}{9} = 8$ cm² {from equation (1)}

Therefore, Tristan is correct, because he needs to find the possible dimensions for rectangle WXYZ and then divide each dimension by 3. (Answer)