Question

sam drew δabc, then applied a scale factor of 2\frac{1}{3} to draw δqrs. diagrams of δabc (right triangle with ab=9, bc=12, ac=15) and δqrs (right triangle with ? marks for qr, rs, qs) what are the side lengths for δqrs? select the box in each row to identify the correct value for each side. options: 11\frac{1}{3}, 14\frac{1}{3}, 17\frac{1}{3}, 21, 28, 35. side qr, side rs, side qs.

Explanation:

Step1: Convert the scale factor to improper fraction

The scale factor is \(2\frac{1}{3}\), which is equal to \(\frac{2\times3 + 1}{3}=\frac{7}{3}\).

Step2: Find the length of side QR

In \(\triangle ABC\), the corresponding side to QR is AB, which has a length of 9. To find QR, we multiply AB by the scale factor: \(9\times\frac{7}{3}= 21\).

Step3: Find the length of side RS

In \(\triangle ABC\), the corresponding side to RS is BC, which has a length of 12. To find RS, we multiply BC by the scale factor: \(12\times\frac{7}{3}= 28\).

Step4: Find the length of side QS

In \(\triangle ABC\), the corresponding side to QS is AC, which has a length of 15. To find QS, we multiply AC by the scale factor: \(15\times\frac{7}{3}= 35\).

Answer:

• Side QR: 21
• Side RS: 28
• Side QS: 35