Question

1. sam drew $\triangle abc$, then applied a scale factor of $2\frac{2}{3}$ to draw $\triangle qrs$.

what are the side lengths of $\triangle qrs$? select the box in each row that identifies the correct value for each side.

	side $qr$	side $rs$	side $qs$
$14\frac{1}{3}$	$\circ$	$\circledcirc$	$\circ$
$17\frac{1}{3}$	$\circledcirc$	$\circ$	$\circ$
$21$	$\circledcirc$	$\circ$	$\circ$
$28$	$\circ$	$\circledcirc$	$\circ$
$35$	$\circ$	$\circ$	$\circledcirc$

Explanation:

Step1: Convert scale factor to improper fraction

The scale factor is \(2\frac{2}{3}\), convert it to an improper fraction: \(2\frac{2}{3}=\frac{2\times3 + 2}{3}=\frac{8}{3}\)

Step2: Find length of QR (corresponds to AB)

Length of AB is 9. So length of QR is \(9\times\frac{8}{3}=24\)? Wait, no, wait the table has 21? Wait, maybe I made a mistake. Wait, AB is 9, BC is 12, AC is 15. Let's check the correspondence. Triangle ABC is right-angled at B, triangle QRS is right-angled at R. So AB corresponds to QR, BC corresponds to RS, and AC corresponds to QS.

So AB = 9, so QR = \(9\times\frac{8}{3}=24\)? But the table has 21? Wait, maybe the scale factor is \(2\frac{1}{3}\)? Wait the original problem says \(2\frac{2}{3}\)? Wait the user's image: "scale factor of \(2\frac{2}{3}\)". Wait maybe I miscalculated. Wait \(9\times\frac{8}{3}=24\), but the table has 21, 28, etc. Wait maybe the scale factor is \(2\frac{1}{3}\)? Wait no, let's re - check.

Wait, maybe the scale factor is \(2\frac{1}{3}=\frac{7}{3}\)? No, the problem says \(2\frac{2}{3}\). Wait, maybe the triangle ABC: AB = 9, BC = 12, AC = 15. Triangle QRS: QR corresponds to AB, RS corresponds to BC, QS corresponds to AC.

So QR: \(9\times\frac{8}{3}=24\)? But the table has 21, 28, 35. Wait 9\times\frac{7}{3}=21, 12\times\frac{7}{3}=28, 15\times\frac{7}{3}=35. Oh! Maybe the scale factor is \(2\frac{1}{3}=\frac{7}{3}\) (maybe a typo in the problem, or my misreading). Let's check: \(2\frac{1}{3}=\frac{7}{3}\). Then:

QR (AB = 9): \(9\times\frac{7}{3}=21\)

RS (BC = 12): \(12\times\frac{7}{3}=28\)

QS (AC = 15): \(15\times\frac{7}{3}=35\)

Which matches the table values (21, 28, 35). So probably the scale factor is \(2\frac{1}{3}\) (maybe a typo in the problem statement as \(2\frac{2}{3}\) was written, but the numbers match with \(\frac{7}{3}\)).

So:

• QR (corresponds to AB = 9): \(9\times\frac{7}{3}=21\)
• RS (corresponds to BC = 12): \(12\times\frac{7}{3}=28\)
• QS (corresponds to AC = 15): \(15\times\frac{7}{3}=35\)

Answer:

• Side QR: 21 (select the option with 21 in the QR column)
• Side RS: 28 (select the option with 28 in the RS column)
• Side QS: 35 (select the option with 35 in the QS column)